Mathematics

Mathematics & Statistics 2011

McGRAW-HILL 2011 CATALOG 

Welcome to McGraw-Hill’s 2011 Mathematics & Statistics Catalog. Inside 

 

 

 

 

 

 

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CONTENTS 

Developmental Mathematics 

Algebra for College Students............................................. 37 

Professional References ............................................... 40 

Arithmetic / Basic Math ........................................................ 3 

Professional References ................................................. 6 

Beginning Algebra ............................................................. 11 


Beginning / Intermediate Algebra Combined ..................... 19 


Intermediate Algebra ......................................................... 29 


PreAlgebra........................................................................... 7 


Mathematics Service Courses 

Business Mathematics....................................................... 53 

Discrete Mathematics ........................................................ 48 

Finite Mathematics ............................................................ 53 

Geometry ........................................................................... 43 


Liberal Arts Mathematics ................................................... 44 

Mathematics for Elementary Teachers .............................. 46 

Technical Mathematics ...................................................... 50 


Precalculus 

College Algebra ................................................................. 57 


College Algebra with Trigonometry .................................... 64 

Precalculus ........................................................................ 67 


Trigonometry ..................................................................... 62 


Calculus 

Applied / Business Calculus .............................................. 79 


Calculus and Analytic Geometry........................................ 81 


Multi-Variable Calculus ...................................................... 93 


Single Variable Calculus .................................................... 87 


Higher Mathematics 

Abstract Algebra .............................................................. 127 

Advanced Calculus .......................................................... 119 

Advanced Engineering Mathematics ............................... 115 

Advanced Geometry ........................................................ 121 

Combinatorics.................................................................. 114 

Complex Analysis ............................................................ 121 

Differential Equations ...................................................... 101 

Professional References ............................................. 103 

Differential Equations with Boundary Value Problems .... 104 


Functional Analysis .......................................................... 124 

Graph Theory .................................................................. 117 

History of Mathematics .................................................... 119 

Introductory Analysis ....................................................... 118 

Linear Algebra ..................................................................111 


Logic ................................................................................ 126 

Mathematical - References.............................................. 126 

Number Theory ................................................................ 120 

Numerical Analysis .......................................................... 120 

Partial Differential Equations ........................................... 106 

Real Analysis ................................................................... 125 

Topology .......................................................................... 127 

Transition to Higher Math / 

Foundations of Higher Math ....................................... 110 

Professional References..............................................111 

Walter Rudin Student Series in Advanced 

Mathematics ............................................................... 108 

i

CONTENTS 

Statistics and Probability 

Advanced Statistics ......................................................... 140 


Applied Statistics - Education, Psychology and 

Social Science ............................................................ 136 

Applied Statistics - Engineering ....................................... 138 


Statistics and Probability (Calculus) ................................ 136 

Statistics and Probability (Non-Calculus) ........................ 131 


Indexes 

Author Index ....................................................................... 149 

Title Index ........................................................................... 143 

ii

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New Titles 

DEVELOPMENTAL MATHEMATICS 

2012 Author ISBN Page 

Basic College Mathematics, 4e Bello 9780073384382 3 

Introductory Algebra, 4e Bello 9780073384399 11 

Algebra for College Students, 6e Dugopolski 9780073384344 37 

Elementary and Intermediate Algebra, 4e Dugopolski 9780073384351 19 

Intermediate Algebra, 7e Dugopolski 9780073384573 29 

Beginning Algebra Messersmith 9780073406169 12 

Beginning and Intermediate Algebra, 3e Messersmith 9780073384375 21 

Intermediate Algebra Messersmith 9780073406176 31 



Hutchinson’s Elementary and Intermediate Algebra, 4e Baratto 9780077350123 23 

Beginning and Intermediate Algebra: The Language and Symbolism of Mathematics, 3e Hall 9780077350048 24 

Beginning Algebra, 3e Miller 9780077349936 14 

Beginning and Intermediate Algebra, 3e Miller 9780077350086 25 

Intermediate Algebra, 3e Miller 9780077349943 32 

Prealgebra Miller 9780077349950 7 

MATHEMATICS SERVICE COURSES 


Mathematics for Elementary Teachers: A Conceptual Approach, 9e Bennett 9780073519579 46 

Mathematics for Elementary Teachers: An Activity Approach, 9e Bennett 9780077430917 47 

Discrete Mathematics and Its Applications, 7e Rosen 9780073383095 48 



Mathematics in Our World, 2e Sobecki 9780077356651 44 

PRECALCULUS 


College Algebra: Graphs and Models Coburn 9780073519548 57 

Precalculus: Graphs and Models Coburn 9780073519531 67 

iii

New Titles 

PRECALCULUS 


College Algebra, 9e Barnett 9780077350161 58 

College Algebra with Trigonometry, 9e Barnett 9780077350109 64 

Precalculus, 7e Barnett 9780077349912 69 

Trigonometry, 2e Coburn 9780077349974 62 

CALCULUS 


Calculus, 4e Smith 9780073383118 81 

Calculus: Early Transcendental Functions, 4e Smith 9780073532325 82, 87, 

93 

HIGHER MATHEMATICS 


Fourier Series and Boundary Value Problems, 8e Brown 9780078035975 106 



Elementary Number Theory, 7e Burton 9780073383149 120 

The History of Mathematics: An Introduction, 7e Burton 9780073383156 119 

STATISTICS AND PROBABILITY 


Elementary Statistics: A Step By Step Approach, 8e Bluman 9780077460396 131 



Statistics for Engineers and Scientists, 3e Navidi 9780073376332 138 

iv

Algebra for College Students..............................................................................37 

Professional References ................................................................................40 

Arithmetic / Basic Math .........................................................................................3 

Professional References ..................................................................................6 

Beginning Algebra ..............................................................................................11 


Beginning / Intermediate Algebra Combined ......................................................19 


Intermediate Algebra ..........................................................................................29 


PreAlgebra............................................................................................................7 



1

New Titles 



Basic College Mathematics, 4e Bello 9780073384382 3 

Introductory Algebra, 4e Bello 9780073384399 11 

Algebra for College Students, 6e Dugopolski 9780073384344 37 

Elementary and Intermediate Algebra, 4e Dugopolski 9780073384351 19 

Intermediate Algebra, 7e Dugopolski 9780073384573 29 

Beginning Algebra Messersmith 9780073406169 12 

Beginning and Intermediate Algebra, 3e Messersmith 9780073384375 21 

Intermediate Algebra Messersmith 9780073406176 31 



Hutchinson’s Elementary and Intermediate Algebra, 4e Baratto 9780077350123 23 

Beginning and Intermediate Algebra: The Language and Symbolism of Mathematics, 3e Hall 9780077350048 24 

Beginning Algebra, 3e Miller 9780077349936 14 

Beginning and Intermediate Algebra, 3e Miller 9780077350086 25 

Intermediate Algebra, 3e Miller 9780077349943 32 

Prealgebra Miller 9780077349950 7 

2


Arithmetic/Basic Math 

NEW 

*9780073384382* 

BASIC COLLEGE 

MATHEMATICS 

4th Edition 

by Ignacio Bello, University of South Florida- 

Tampa 

2012 (January 2011) / 704 pages 

ISBN: 9780073384382 

mhhe.com/math/devmath/bello/ 

Basic College Mathematics, 4e will be a review of fundamental math 

concepts for some students and may break new ground for others. 

 

refreshing book that appeals to all learning styles and reaches out to 

diverse demographics. Through down-to-earth explanations, patient 

skill-building, and exceptionally interesting and realistic applications, 

this worktext will empower students to learn and master mathematics 

in the real world. 

NEW TO THIS EDITION 

These examples illustrate important and contemporary applications 

of mathematics concerning the environment, ecology and climate 

change, what we will call “The Green Math.” These applications will be 

clearly marked so you can pay special attention to them. They appear 

at the end of each and every section and will have corresponding 

problems in the Exercises. 

FEATURES 

Bello student oriented applications includes topics that students 

are familiar with and use on a regular basis. The applications are kept 

up-to-date and relevant for a continually changing student population. 

Bello is even successful at making the applications even more student 

friendly by adding a touch a humor when appropriate. 

Gives students a reliable helpful tool in demystifying word problems 

so that they can more readily translate them into equations they 

can recognize and solve. 

Connects the computation process they learned throughout a lesson 

to the use of calculator with the intended focus being conceptual 

understanding as opposed to computational work. 

Section openers include page references for prerequisite material, 

list of objectives, and “Getting Started” applications to motivate 

section content. 

End-of-section exercise sets to include exercises keyed to objectives 

and to examples, applied exercises, and “skill checkers” to 

confirm/reinforce skills needed for the next section. 

Writing exercises give students the opportunity to express 

mathematical concepts and procedures in their own words, thereby 

expressing and verbalizing what they have learned--available at the 

end of each chapter. 

Written to have a flexible set of teaching tools and pedagogical 

features that instructors and students can adapt to their own learning 

styles. English is Bello’s second language and because of this Bello 

is able to use his learning experiences to communicate to students 

in a format they are comfortable with able to understand. 

CONTENTS 

1. WHOLE NUMBERS 

1.1 Standard Numerals 

1.2 Ordering and Rounding Whole Numbers 

1.3 Addition 

1.4 Subtraction 

1.5 Multiplication 

1.6 Division 

1.7 Primes, Factors, and Exponents 

1.8 Order of Operations and Grouping Symbols 

1.9 Equations and Problem Solving 

2. FRACTIONS AND MIXED NUMBERS 

2.1 Fractions and Mixed Numbers 

2.2 Equivalent Fractions: Building and Reducing 

2.3 Multiplication and Division of Fractions and Mixed Numbers 

2.4 The Lease Common Multiple (LCM) 

2.5 Addition and Subtraction of Mixed Numbers 

2.6 Order of Operations and Grouping Symbols 


3. DECIMALS 

3.1 Addition and Subtraction of Decimals 

3.2 Multiplication and Division of Decimals 

3.3 Fractions and Decimals 

3.4 Decimals, Fractions, and Order of Operations 


4. RATIO, RATE, AND PROPORTION 

4.1 Ratio 

4.2 Rates 

4.3 Proportion 

4.4 Problem Solving Involving Proportions 

5. PERCENT 

5.1 Percent Notation 

5.2 Percent Problems 

5.3 Solving Percent Problems Using Proportions 

5.4 Taxes, Interest, Commissions, and Discounts 

5.5 Applications: Percent of Increase or Decrease 

5.6 Consumer Credit 

6. STATISTICS AND GRAPHS 

6.1 Tables and Pictographs 

6.2 Bar and Line Graphs 

6.3 Circle Graphs (Pie Charts) 

6.4 Mean, Median, and Mode 

7. MEASUREMENT AND THE METRIC SYSTEM 

7.1 Length: U.S. System 

7.2 Length: The Metric System 

7.3 Length: U.S. to Metric and Metric to U.S. Conversions 

7.4 Area: U.S., Metric, and Conversions 

7.5 Volume (Capacity): U.S., Metric, and Conversions 

7.6 Weight and Temperature: U.S., Metric, and Conversions 

8. GEOMETRY 

8.1 Lines, Angles, and Triangles 

8.2 Finding Perimeters 

8.3 Finding Areas 

8.4 Volumes of Solids 

8.5 Square Roots and the Pythagorean Theorem 

9. THE REAL NUMBERS 

9.1 Addition and Subtraction of Integers 

9.2 Multiplication and Division of Integers 

9.3 The Rational Numbers 

9.4 Order of Operations 

10. INTRODUCTION TO ALGEBRA 

10.1 Introduction to Algebra 

10.2 The Algebra of Exponents 

10.3 Scientific Notation 

10.4 Solving Linear Equations 

10.5 Applications: Word Problems 

3


HUTCHINSON’S BASIC MATHEMATICAL 

SKILLS WITH GEOMETRY 

8th Edition 

By Stefan Baratto, Clackamas Community College, Barry Bergman, and 

Donald Hutchison 

2010 (October 2009) / Softcover / 832 pages 

ISBN: 9780077354749 

www.mhhe.com/baratto 

Basic Mathematical Skills with Geometry, 8/e by Baratto/Bergman 

is part of the latest offerings in the successful Hutchison Series in 

Mathematics. The eigth edition continues the hallmark approach of 

encouraging the learning of mathematics by focusing its coverage on 

mastering math through practice. This worktext seeks to provide carefully 

detailed explanations and accessible pedagogy to introduce basic 

mathematical skills and put the content in context. The authors use a 

three-pronged approach (I. Communication, II. Pattern Recognition, 

and III. Problem Solving) to present the material and stimulate critical 

thinking skills. Items such as Math Anxiety boxes, Check Yourself 

exercises, and Activities represent this approach and the underlying 

philosophy of mastering math through practice. The exercise sets 

have been expanded, organized, and clearly labeled. Vocational 

and professional-technical exercises have been added throughout. 

Repeated exposure to this consistent structure should help advance 

the student’s skills in relating to mathematics. The book is designed 

for a one-semester basic math course and is appropriate for lecture, 

learning center, laboratory, or self-paced courses. It is accompanied 

by numerous useful supplements, including McGraw-Hill’s online 

homework management system, MathZone. 

CONTENTS 

1 Operations on Whole Numbers 

1.1 The Decimal Place-Value System 

1.2 Addition 

1.3 Subtraction 

1.4 Rounding, Estimation, and Order 


1.6 Division 

1.7 Exponential Notation and the Order of Operations 

2 Multiplying and Dividing Fractions 

2.1 Prime Numbers and Divisibility 

2.2 Factoring Whole Numbers 

2.3 Fraction Basics 

2.4 Simplifying Fractions 

2.5 Multiplying Fractions 

2.6 Dividing Fractions 

3 Adding and Subtracting Fractions 

3.1 Adding and Subtracting Fractions with Like Denominators 

3.2 Common Multiples 

3.3 Adding and Subtracting Fractions with Unlike Denominators 

3.4 Adding and Subtracting Mixed Numbers 

3.5 Order of Operations with Fractions 

3.6 Estimation Applications 

4 Decimals 

4.1 Place Value and Rounding 

4.2 Converting Between Fractions and Decimals 

4.3 Adding and Subtracting Decimals 

4.4 Multiplying Decimals 

4.5 Dividing Decimals 

5 Ratios and Proportions 

5.1 Ratios 

5.2 Rates and Unit Pricing 

5.3 Proportions 

5.4 Solving Proportions 

6 Percents 

6.1 Writing Percents as Fractions and Decimals 

6.2 Writing Decimals and Fractions as Percents 

6.3 Identifying the Parts of a Percent Problem 

6.4 Solving Percent Problems 

7 Measurement 

7.1 The Units of the English System 

7.2 Metric Units of Length 

7.3 Metric Units of Weight and Volume 

7.4 Converting Between the English and Metric Systems 

8 Geometry 

8.1 Area and Circumference 

8.2 Lines and Angles 

8.3 Triangles 


9 Data Analysis and Statistics 

9.1 Means, Medians, and Modes 

9.2 Tables, Pictographs, and Bar Graphs 

9.3 Line Graphs and Predictions 

9.4 Creating Bar Graphs and Pie Charts 

9.5 Describing and Summarizing Data Sets 

10 The Real Number System 

10.1 Real Numbers and Order 

10.2 Adding Real Numbers 

10.3 Subtracting Real Numbers 

10.4 Multiplying Real Numbers 

10.5 Dividing Real Numbers and the Order of Operations 

11 An Introduction to Algebra 

11.1 From Arithmetic to Algebra 

11.2 Evaluating Algebraic Expressions 

11.3 Adding and Subtracting Algebraic Expressions 

11.4 Using the Addition Property to Solve an Equation 

11.5 Using the Multiplication Property to Solve an Equation 

11.6 Combining the Properties to Solve Equations 

BASIC COLLEGE MATHEMATICS 

2nd Edition 

by Julie Miller, Daytona State College-Daytona Beach, Molly O’Neill, 

Daytona State College-Daytona Beach, and Nancy Hyde 

2009 (October 2008) / Paper / 832 pages 

ISBN: 9780077281137 

www.mhhe.com/moh 

Basic College Mathematics offers a refreshing approach to the traditional 

content of the course. Presented in worktext format, Basic 

College Mathematics focuses on basic number skills: operations and 

problem-solving with whole numbers, fractions, and decimals. Other 

topics include geometry, measurement, ratios, proportions, percents, 

and the real number system (with an introduction to algebra). The text 

 

 

mental level students. 

CONTENTS 

Chapter 1: Whole Numbers 

1.1 Introduction to Whole Numbers 

1.2 Addition of Whole Numbers and Perimeter 

1.3 Subtraction of Whole Numbers 

1.4 Rounding and Estimating 

1.5 Multiplication of Whole Numbers and Area 

1.6 Division of Whole Numbers Problem Recognition Exercises – 

Operations on Whole Numbers 

1.7 Exponents, Square Roots, and the Order of Operations 

1.8 Problem-Solving Strategies 

Chapter 2: Fractions and Mixed Numbers: Multiplication and Division 

2.1 Introduction to Fractions and Mixed Numbers 

2.2 Prime Numbers and Factorizations 

2.3 Simplifying Fractions to Lowest Terms 

2.4 Multiplication of Fractions and Applications 

2.5 Division of Fractions and Applications Problem Recognition Exercises 

– Multiplication and Division of Fractions 

2.6 Multiplication and Division of Mixed Numbers 

Chapter 3: Fractions and Mixed Numbers: Addition and Subtraction 

3.1 Addition and Subtraction of Like Fractions 

3.2 Least Common Multiple and Equivalent Fractions 

3.3 Addition and Subtraction of Unlike Fractions 

3.4 Addition and Subtractions of Mixed Numbers Problem Recognition 

4


Exercises – Operations on Fractions and Mixed Numbers 

3.5 Order of Operations and Applications of Fractions and Mixed 

Numbers 

Chapter 4: Decimals 

4.1 Decimal Notation and Rounding 


4.3 Multiplication of Decimals 

4.4 Division of Decimals Problem Recognition Exercises – Operations 

on Decimals 

4.5 Fractions as Decimals 

4.6 Order of Operations and Applications of Decimals 

Chapter 5: Ratio and Proportion 

5.1 Ratios 

5.2 Rates Problem Recognition Exercises – Ratios and Rates 


5.4 Applications of Proportions and Similar Figures 

Chapter 6: Percents 

6.1 Percents and Their Fraction and Decimal Forms 

6.2 Fractions and Decimals and Their Percent Forms 

6.3 Percent Proportions and Applications 

6.4 Percent Equations and Applications Problem Recognition 

Exercises--Percents 

6.5 Applications Involving Tax and Commission 

6.6 Percent Increase and Decrease 

6.7 Simple and Compound Interest 

Chapter 7: Measurement 

7.1 Converting U.S. Customary Units of Length 

7.2 Converting U.S. Customary Units of Time, Weight, and Capacity 

7.3 Metric Units of Length 

7.4 Metric Units of Mass and Capacity and Medical Applications 

Problem Recognition Exercises – Conversion of Units 

7.5 Converting Between U.S. Customary and Metric Units 

Chapter 8: Geometry 


8.2 Triangles and the Pythagorean Theorem 

8.3 Quadrilaterals, Perimeter, and Area 

8.4 Circles, Circumference, and AreaProblem Recognition Exercises 

– Perimeter, Circumference, and Area 

8.5 Volume 

Chapter 9: Introduction to Statistics 

9.1 Tables, Bar Graphs, Pictographs, and Line Graphs 

9.2 Frequency Distributions and Histograms 

9.3 Circle Graphs Problem Recognition Exercises – Tables and 

Graphs 


9.5 Introduction to Probability 

Chapter 10: Real Numbers 

10.1 Real Numbers and the Real Number Line 

10.2 Addition of Real Numbers 

10.3 Subtraction of Real Numbers Problem Recognition Exercises – 

Addition and Subtraction of Real Numbers 

10.4 Multiplication and Division of Real Numbers Problem Recognition 

Exercises – Multiplication and Division of Real Numbers 


Chapter 11: Solving Equations 

11.1 Properties of Real Numbers 

11.2 Simplifying Expressions 

11.3 Addition and Subtraction Properties of Equality 

11.4 Multiplication and Division Properties of Equality 

11.5 Solving Equations with Multiple Steps Problem Recognition 

Exercises – Linear Equations 

11.6 Applications and Problem Solving 

Appendix 

A.1 Energy and Power 

A.2 Scientific Notation 

A.3 Rectangular Coordinate System 

SCHAUM’S A-Z MATHEMATICS 

By John Berry; Ted Graham and Elizabeth Berry 

2004 / 288 pages 

ISBN: 9780071419369 

A Schaum’s Publication 

Schaum’s A-Z handbooks make excellent complements to course 

textbooks and test preparation guides. Ideal for ambitious high school 

seniors—especially AP students—and college freshmen, they feature 

 

terms and phrases that help students quickly break through the jargon 

barrier. Clear explanations of key concepts, supplemented with lucid 

illustrations, help build mastery of theory and provide a ready reference 

to supplement class work. 

SCHAUM’S OUTLINE OF REVIEW OF 

ELEMENTARY MATHEMATICS 

2nd Edition 

By Barnett Rich (deceased), Philip Schmidt, State University College— 

New Paltz 

1997 / 288 pages 

ISBN: 9780070522794 

(A Schaum’s Publication) 

http://books.mcgraw-hill.com/cgi-bin/getbook.pl?isbn=0070522790& 

adkey=W02003 

CONTENTS 

Fundamentals of Arithmetic: Number 

Fundamentals of Arithmetic and Introduction to Calculators 

Fractions 

Decimals 

Percents 

Signed Numbers 

Fundamentals of Algebra: Laws and Operations 

Fundamentals of Algebra: Equations and Formulas 

Ratios, Proportions, and Rates. Fundamentals of Geometry 

Invitation to Publish 

McGraw-Hill is interested in reviewing textbook 

proposals for publication. 

 

email to asiapub@mcgraw-hill.com. 

Visit McGraw-Hill Education (Asia) 

Website: http://www.mheducation.asia/publish/ 

5


Professional References 

ARITHMETIC AND ALGEBRA AGAIN 

2nd Edition 

By Brita Immergut, La Guardia Community College and Jean Burr-Smith 

2005 / 400 pages 

ISBN: 9780071435338 

(A Professional Reference Title) 

CONTENTS 

Part One. Arithmetic 

1. The Arithmetic of Whole Numbers 

2. Integers 

3. Decimals and Percents 

4. Fractions 

5. Measurements 

6. Basic Operations 

7. Equations and Inequalities 

8. Graphing 

9. Word Problems 

Part Two. Practical Mathematics 

10. Applications 

11. Mathematics in Banking 

12. Statistics 

13. Probability 

14. Calculators 

MATH WORD PROBLEMS DEMYSTIFIED 

By Allan G Bluman 

2004 / 308 pages 

ISBN: 9780071443166 


CONTENTS 

Preface 

Lesson 1: Introduction to Solving Word Problems 

Lesson 2: Solving Word Problems Using Whole Numbers 

REFRESHER I: DECIMALS 

Lesson 3: Solving Word Problems Using Decimals 

REFRESHER II: FRACTIONS 

Lesson 4: Solving Word Problems Using Fractions 

QUIZ 1 

REFRESHER III: PERCENTS 

Lesson 5: Solving Word Problems Using Percents 

Lesson 6: Solving Word Problems Using Proportions 

Lesson 7: Solving Word Problems Using Formulas 

QUIZ 2 

REFRESHER IV: EQUATIONS 

Lesson 8: Algebraic Representation 

Lesson 9: Solving Number Problems 

Lesson 10: Solving Digit Problems 

Lesson 11: Solving Coin Problems 

QUIZ 3 

Lesson 12: Solving Age Problems 

Lesson 13: Solving Distance Problems 

Lesson 14: Solving Mixture Problems 

Lesson 15: Solving Finance Problems 

Lesson 16: Solving Lever Problems 

Lesson 17: Solving Work Problems 

QUIZ 4 

REFRESHER V: SYSTEMS OF EQUATIONS 

Lesson 18: Solving Word Problems Using Two Equations 

REFRESHER VI: QUADRATIC EQUATIONS 

Lesson 19: Solving Word Problems Using Quadratic Equations 

Lesson 20: Solving Word Problems in Geometry 

QUIZ 5 

Lesson 21: Solving Word Problems Using Other Strategies 

Lesson 22: Solving Word Problems in Probability 

Lesson 23: Solving Word Problems in Statistics 

QUIZ 6 

FINAL EXAM 

ANSWER TO QUIZZES AND FINAL EXAM 

SUPPLEMENT: SUGGESTIONS FOR SUCCESS IN MATHEMATICS 

INDEX 

EVERYDAY MATH DEMYSTIFIED 

By Stan Gibilisco 

2004 / 440 pages 

ISBN: 9780071431194 


CONTENTS 

PART ONE: EXPRESSING QUANTITIES 

Chapter 1. Numbers and Arithmetic 

Chapter 2. How Variables Relate 

Chapter 3. Extreme Numbers 

Chapter 4. How Things Are Measured 

Test: Part One 

PART TWO: FINDING UNKNOWNS 

Chapter 5. Basic Algebra 

Chapter 6. More Algebra 

Chapter 7. A Statistics Sampler 

Chapter 8. Taking Chances 

Test: Part Two 

PART THREE: SHAPES AND PLACES 

Chapter 9. Geometry on the Flats 

Chapter 10. Geometry in Space 

Chapter 11. Graphing It 

Chapter 12. A Taste of Trigonometry 

Test: Part Three 

PART FOUR: MATH IN SCIENCE 

Chapter 13. Vectors and 3D 

Chapter 14. Growth and Decay 

Chapter 15. How Things Move 

Test: Part Four 

Final Exam 

Answers to Quiz, Test, and Exam Questions 

Suggested Additional References 

Index 

HOW TO SOLVE MATH WORD PROBLEMS 

ON STANDARDIZED TESTS 

By David Wayne 

2002 / 304 pages 

ISBN: 9780071376938 


This is an indispensable resource for the parents of the more than 16 

million school children nationwide who, each year, take standardized 

assessment tests of basic math and language skills. It focuses on the 

category of test question that students dread the most and in which 

they do least well: mathematics word problems. Written by a national 

expert in mathematics education, it takes the fear and frustration out 

of mathematics word problems by providing a simple, step-by-step 

approach that emphasizes the mechanics and grammar of problem 

solving and that is guaranteed to make solving all types of math word 

problems a breeze, even for math-phobic students. 

Covers all types of mathematics word problems found on standardized 

tests and identifies the value of each type on the tests 

6


Features dozens of examples and practice problems, with stepby-step 

solutions and key mathematics concepts clearly explained 

Includes a 50-question drill using problems drawn from actual 

tests, with answers provided at the back of the book 

HOW TO SOLVE WORD PROBLEMS IN 

MATHEMATICS 

By David S Wayne 

2001 / 164 pages 

ISBN: 9780071362726 


CONTENTS 

Chapter 1: Measurement, Estimation, and Using Formulas. 

Chapter 2: Using Algebraic Equations to Solve Problems. 

Chapter 3: Word Problems Involving Ratio, Proportion, and Percentage. 

Chapter 4: Word Problems Involving Geometry and Trignometry. 

Chapter 5: Word Problems Involving Statistics, Counting, and Probability. 

Chapter 6: Miscellaneous Problem Drill. 

Appendix: A Brief Review of Solving Equations. 

PreAlgebra 

NEW *9780077349950* 

PREALGEBRA 

by Julie Miller, Molly O’Neill, and Nancy Hyde, 

Daytona State College 

2011 (January 2010) / Softcover / 752 pages 

ISBN: 9780077349950 


 

Miller/O’Neill/Hyde Prealgebra will introduce algebraic concepts 

early and repeat them as student would work through a Basic College 

Mathematics (or arithmetic) table of contents. Prealegbra is the 

ground work that’s needed for developmental students to take the 

next step into a traditional algebra course. 

According to our market Julie and Molly’s greatest strength is the ability 

to conceptualize algebraic concepts. The goal of this textbook will be 

to help student conceptualize the mathematics and it’s relevancy in 

everything from their daily errands to the workplace. 

Prealgebra can be considered a derivative of Basic College Mathematics. 

One new chapter introducing the variable and equations is 

needed. Each subsequent chapter is basic mathematics/arithmetic 

content with additional sections containing algebra incorporated 

throughout. 

CONTENTS 


Section 1.1 Study Tips 

Group Activity – Becoming a Successful Student 

Section 1.2 Introduction to Whole Numbers 

Section 1.3 Addition and Subtraction of Whole Numbers and Perimeter 

Section 1.4 Rounding and Estimating 

Section 1.5 Multiplication of Whole Numbers and Area 

Section 1.6 Division of Whole Numbers 

Problem Recognition Exercises – Operations on Whole Numbers 

Section 1.7 Exponents, Variables, and the Order of Operations 

Section 1.8 Mixed Applications and Computing Mean 

Chapter 2: Integers and Algebraic Expressions 

Section 2.1 Integers, Absolute Value, and Opposite 

Section 2.2 Addition of Integers 

Section 2.3 Subtraction of Integers 

Section 2.4 Multiplication and Division of Integers Problem Recognition 

Exercises – Operations on Integers 

Section 2.5 Order of Operations and Algebraic Expressions 

Group Activity – Checking Weather Conditions 

Chapter 3: Solving Equations 

Section 3.1 Simplifying Expressions and Combining Like Terms 

Section 3.2 Addition and Subtraction Properties of Equality 

Section 3.3 Multiplication and Division Properties of Equality 

Section 3.4 Solving Equations with Multiple Steps 

Problem Recognition Exercises – Simplifying Expressions and Solving 

Equations 

Section 3.5 Applications and Problem Solving 

Group Activity – Constructing Linear Equations 

Chapter 4: Fractions and Mixed Numbers 

Section 4.1 Introduction to Fractions and Mixed Numbers 

Section 4.2 Simplifying Fractions 

Section 4.3 Multiplication and Division of Fractions 

Section 4.4 Least Common Multiple and Equivalent Fractions 

Section 4.5 Addition and Subtraction of Fractions 

Section 4.6 Estimation and Operations on Mixed Numbers Problem 

Recognition Exercises – Operations on Fractions and Mixed Numbers 

Section 4.7 Order of Operations and Complex Fractions 

Section 4.8 Solving Equations Containing Fractions Problem Recognition 

Exercises – Comparing Equations and Expressions 

Group Activity – Card Games with Fractions 

Chapter 5: Decimals 

Section 5.1 Decimal Notation and Rounding 

Section 5.2 Addition and Subtraction of Decimals 

Section 5.3 Multiplication of Decimals and Applications with Circles 

Section 5.4 Division of Decimals Problem Recognition Exercises – 

Operations on Decimals 

Section 5.5 Fractions, Decimals, and the Order of Operations 

Section 5.6 Solving Equations Containing Decimals 

Section 5.7 Mean, Median, and Mode 

Group Activity – Purchasing from a Catalog 

Chapter 6: Ratio and Proportion 

Section 6.1 Ratios 

Section 6.2 Rates 

Section 6.3 Proportions 

Problem Recognition Exercises: Operations on Fractions Versus 

Solving Proportions 

Section 6.4 Applications of Proportions and Similar Figures 

Group Activity – Investigating Probability 

Chapter 7: Percents 

Section 7.1 Percents, Fractions, and Decimals 

Section 7.2 Percent Proportions and Applications 

Section 7.3 Percent Equations and Applications 

Problem Recognition Exercises – Percents 

Section 7.4 Applications of Sales Tax, Commission, Discount, Markup, 

and Percent Increase and Decrease 

Section 7.5 Simple and Compound Interest Group Activity – Tracking 

Stocks 

Chapter 8: Measurement and Geometry 

Section 8.1 U.S. Customary Units of Measurement 

Section 8.2 Metric Units of Measurement 

7


Section 8.3 Converting Between U.S. Customary and Metric Units 

Problem Recognition Exercises – U.S. Customary and Metric Conversions 

Section 8.4 Medical Applications Involving Measurement 

Section 8.5 Lines and Angles 

Section 8.6 Triangles and the Pythagorean Theorem 

Section 8.7 Perimeter, Circumference, and Area Problem Recognition 

Exercises – Area, Perimeter, and Circumference 

Section 8.8 Volume and Surface Area Group Activity – Remodeling 

the Classroom 

Chapter 9: Graphs and Statistics 

Section 9.1 Rectangular Coordinate System 

Section 9.2 Graphing Two Variable Equations 

Section 9.3 Tables, Bar Graphs, Pictographs, and Line Graphs 

Section 9.4 Frequency Distributions and Histograms 

Section 9.5 Circle Graphs 

Section 9.6 Introduction to Probability 

Group Activity – Creating a Statistical Report 

Chapter 10 Exponents and Polynomials 

Section 10.1 Addition and Subtraction of Polynomials 

Section 10.2 Multiplication Properties of Exponents 

Section 10.3 Multiplication of Polynomials 

Problem Recognition Exercises – Operations on Polynomials and 

Exponential Expressions 

Section 10.4 Introduction to Factoring 

Section 10.5 Negative Exponents and the Quotient Rule for Exponents 

Section 10.6 Scientific Notation 

Group Activity – Evaluating and Interpreting a Polynomial Model 

PREALGEBRA 

Media Enhanced Edition, 3rd Edition 

by Stefan Baratto, Clackamas Community College, Barry Bergman, and 

Donald Hutchison 

2010 (January 2009) / 896 pages 

ISBN: 9780077299620 

ISBN: 9780077320355 (Prepack with Mathzone Student Access 

Card) 

www.mhhe.com/hutchison 

Prealgebra: Media Enhanced Edition, 3e by Baratto/Bergman is the 

latest offering from authors Stefan Baratto and Barry Bergman. This 

media enhanced edition of Prealgebra focuses on mastering math 

through practice with the integration of the ALEKS® software. ALEKS 

helps to remediate students who may have a lack of prerequisite 

 

engine. ALEKS provides students with a map (pictorial graph) of their 

progress to identify mathematical skills they have mastered and skills 

where remediation is required. Icons accompany exercises in the text 

where a similar problem is available in ALEKS. 

CONTENTS 

CHAPTER 1 Whole Numbers 

Pretest Chapter 1 

1.1 Introduction to Whole Numbers and Place Value 

1.2 Addition of Whole Numbers 


1.4 Rounding, Estimation, and Ordering of Whole Numbers 

1.5 Multiplication of Whole Numbers 

1.6 Division of Whole Numbers 

1.7 Exponents and Whole Numbers 

1.8 Grouping Symbols and the Order of Operations 

1.9 An Introduction to Equations 

Summary 

Summary Exercises 

Self-Test for Chapter 1 

CHAPTER 2 Integers and Introduction to Algebra 


2.1 Introduction to Integers 

2.2 Addition of Integers 

2.3 Subtraction of Integers 

2.4 Multiplication of Integers 

2.5 Division of Integers 

2.6 Introduction to Algebra: Variables and Expressions 


2.8 Simplifying Algebraic Expressions 

2.9 Introduction to Linear Equations 

2.10 The Addition Property of Equality 

Summary 



Cumulative Review for Chapters 1 to 2 

CHAPTER 3 Fractions and Equations 


3.1 Introduction to Fractions 

3.2 Prime Numbers and Factorization 

3.3 Equivalent Fractions 

3.4 Multiplication and Division of Fractions 

3.5 The Multiplication Property of Equality 

3.6 Linear Equations in One Variable 

Summary 




CHAPTER 4 Applications of Fractions and Equations 


4.1 Addition and Subtraction of Fractions 

4.2 Operations on Mixed Numbers 

4.3 Applications Involving Fractions 

4.4 Equations Containing Fractions 

4.5 Applications of Linear Equations in One Variable 

4.6 Complex Fractions (optional) 

Summary 




CHAPTER 5 Decimals 


5.1 Introduction to Decimals, Place Value, and Rounding 



5.4 Division of Decimals 


5.6 Equations Containing Decimals 


5.8 Applications 

Summary 




CHAPTER 6 Ratio, Rate, and Proportion 


6.1 Ratios 

6.2 Rates 


6.4 Similar Triangles and Proportions 

6.5 Linear Measurement and Conversion 

Summary 




CHAPTER 7 Percent 


7.1 Percents, Decimals, and Fractions 


7.3 Solving Percent Applications Using Equations 

7.4 Applications: Simple and Compound Interest 

7.5 More Applications of Percent 

Summary 



8



CHAPTER 8 Geometry 



8.2 Perimeter and Circumference 

8.3 Area and Volume 

Summary 




CHAPTER 9 Graphing and Introduction to Statistics 


9.1 Tables and Graphs of Data 

9.2 The Rectangular Coordinate System 

9.3 Linear Equations in Two Variables 


Summary 




CHAPTER 10 Polynomials 


10.1 Properties of Exponents 

10.2 Introduction to Polynomials 

10.3 Addition and Subtraction of Polynomials 

10.4 Multiplying Polynomials 

10.5 Introduction to Factoring Polynomials 

Summary 



Practice Final Exam 

PREALGEBRA 

2nd Edition 

By Donald Hutchison, Barry Bergman, and Stefan Baratto, all of Clackamas 

Community College 

2007 (December 2005) / Softcover / 896 pages 

ISBN: 9780073250335 (with MathZone) 

www.mhhe.com/streeter 

CONTENTS 

CHAPTER 1 Whole Numbers 


1.1 Introduction to Whole Numbers, Place Value 

1.2 Addition of Whole Numbers 


1.4 Rounding, Estimation, and Ordering of Whole Numbers 

1.5 Multiplication of Whole Numbers 

1.6 Division of Whole Numbers 

1.7 Exponents 


1.9 An Introduction to Equations 

Summary 

Summary and Review Exercises 

Chapter Test 

CHAPTER 2 Integers and Introduction to Algebra 


2.1 Introduction to Integers 

2.2 Addition of Integers 

2.3 Subtraction of Integers 

2.4 Multiplication of Integers 

2.5 Division of Integers 

2.6 Introduction to Algebra: Variables and Expressions 


2.8 Simplifying Algebraic Expressions 

2.9 Introduction to Linear Equations 

2.10 The Addition Property of Equality 

Summary 


Chapter Test 

Cumulative Test for Chapters 1 and 2 

CHAPTER 3 Fractions and Equations 



3.2 Prime Numbers and Factorization 

3.3 Equivalent Fractions 

3.4 Multiplication and Division of Fractions 

3.5 The Multiplication Property of Equality 


Summary 


Chapter Test 

Cumulative Test for Chapters 1 to 3 

CHAPTER 4 Applications of Fractions and Equations 


4.1 Addition and Subtraction of Fractions 

4.2 Operations on Mixed Numbers 

4.3 Complex Fractions 

4.4 Applications Involving Fractions 

4.5 Equations Containing Fractions 


Summary 


Chapter Test Cumulative Test for Chapters 1 to 4 

CHAPTER 5 Decimals 


5.1 Introduction to Decimals, Place Value, and Rounding 



5.4 Division of Decimals 


5.6 Equations Containing Decimals 



Summary 



CHAPTER 6 Ratio, Rate, and Proportion 


6.1 Ratios 

6.2 Rates 


6.4 Similar Triangles and Proportions 

6.5 More Applications of Proportion 

6.6 Linear Measurement and Conversion 

Summary 



CHAPTER 7 Percent 


7.1 Percents, Decimals, and Fractions 


7.3 Solving Percent Applications Using Equations 

7.4 Applications: Simple and Compound Interest 

7.5 More Applications of Percent Summary 



CHAPTER 8 Geometry 



8.2 Perimeter and Circumference 

8.3 Area and Volume 

Summary 


Chapter Test. Cumulative Test for Chapters 1 to 8 

CHAPTER 9 Graphing and Introduction to Statistics 


9.1 Circle Graphs 

9.2 Pictographs, Bar Graphs, and Line Graphs 

9





Summary 


Chapter Test. Cumulative Test for Chapters 1 to 9 

CHAPTER 10 Polynomials 





10.4 Introduction to Factoring Polynomials 

Summary 


Chapter Test. Practice Final Exam Chapters 1 to 10 



2nd Edition 


2005 / 400 pages 

ISBN: 9780071435338 


CONTENTS 



2. Integers 


4. Fractions 




8. Graphing 










2004 / 308 pages 

ISBN: 9780071443166 


CONTENTS 

Preface 







QUIZ 1 





QUIZ 2 






QUIZ 3 







QUIZ 4 






QUIZ 5 




QUIZ 6 

FINAL EXAM 



INDEX 




2002 / 304 pages 

ISBN: 9780071376938 


















10



MATHEMATICS 


2001 / 164 pages 

ISBN: 9780071362726 


CONTENTS 








Beginning Algebra 

NEW *9780073384399* 

INTRODUCTORY ALGEBRA 

4th Edition 

by Ignacio Bello 

2012 (January 2011) / 800 pages 

ISBN: 9780073384399 

mhhe.com/math/devmath/bello/ 

Introductory Algebra, 4e will be a review of fundamental math 

concepts for some students and may break new ground for others. 

 

refreshing book that appeals to all learning styles and reaches out to 

diverse demographics. Through down-to-earth explanations, patient 

skill-building, and exceptionally interesting and realistic applications, 

this worktext will empower students to learn and master mathematics 

in the real world. 


Green Math: This edition features new Green Math Examples 

and Green Math Applications, which provide students with the ability 

to apply mathematics to topics present in all aspects of their lives. 

Every day people see media reports about the environment, fill their 

car’s tank with gasoline, and make choices about what products they 

purchase. Green Math Examples and Applications teach students how 

to make and interpret these choices mathematically. The book was 

printed on paper that is 10% post consumer waste. 

Green Math Examples illustrate important and contemporary 

applications of mathematics concerning the environment, ecology 

and climate change. They usually appear as the last example in 

each section and are marked with a distinct Green Math icon. The 

Green Math Applications, also clearly marked, appear in the end of 

section problems. 

FEATURES 

Bello student oriented applications includes topics that students 

are familiar with and use on a regular basis. The applications are kept 

up-to-date and relevant for a continually changing student population. 

Bello is even successful at making the applications even more student 

friendly by adding a touch a humor when appropriate. 

Gives students a reliable helpful tool in demystifying word problems 

so that they can more readily translate them into equations they 

can recognize and solve. 

Connects the computation process they learned throughout a lesson 

to the use of calculator with the intended focus being conceptual 

understanding as opposed to computational work. 

Section openers include page references for prerequisite material, 

list of objectives, and “Getting Started” applications to motivate 

section content. 

End-of-section exercise sets to include exercises keyed to objectives 

and to examples, applied exercises, and “skill checkers” to 

confirm/reinforce skills needed for the next section. 

Writing exercises give students the opportunity to express 

mathematical concepts and procedures in their own words, thereby 

expressing and verbalizing what they have learned--available at the 

end of each chapter. 

Written to have a flexible set of teaching tools and pedagogical 

features that instructors and students can adapt to their own learning 

styles. English is Bello’s second language and because of this Bello 

is able to use his learning experiences to communicate to students 

in a format they are comfortable with able to understand. 

CONTENTS 

R. Prealgebra Review 

R.1. Fractions: Building and Reducing 

R.2. Operations with Fractions and Mixed Numbers 

R.3. Decimals and Percents 

1. Real Numbers and Their Properties1.1 Introduction to Algebra 

1.2 The Real Numbers 

1.3 Adding and Subtracting Real Numbers 

1.4 Multiplying and Dividing Real Numbers 


1.6 Properties of the Real Numbers 


2. Equations, Problem Solving, and Inequalities2.1 The Additions and 

Subtraction Properties of Equality 

2.2 The Multiplication and Division Properties of Equality 

2.3 Linear Equations 

2.4 Problem Solving: Integer, General, and Geometry Problems 

2.5 Problem Solving: Motion, Mixture, and Investment Problems 

2.6 Formulas and Geometry Applications 

2.7 Properties of Inequalities 

3. Graphs of Linear Equations, Inequalities, and Applications3.1 Line 

Graphs, Bar Graphs, and Applications 

3.2 Graphing Linear Equations in Two Variables 

3.3 Graphing Lines Using Intercepts: Horizontal and Vertical Lines 

3.4 The Slope of a Line: Parallel and Perpendicular Lines 

3.5 Graphing Lines Using Points and Slope 

3.6 Applications of Equations of Lines 

3.7 Graphing Inequalities in Two Variables 

4. Exponents and Polynomials4.1 The Product, Quotient, and Power 

Rules for Exponents 

4.2 Integer Exponents 

4.3 Application of Exponents: Scientific Notation 

4.4 Polynomials: An Introduction 


4.6 Multiplication of Polynomials 

4.7 Special Products of Polynomials 

11


4.8 Division of Polynomials 

5. Factoring5.1 Common Factors and Grouping 

5.2 Factoring x2 + bx + c 

5.3 Factoring ax2 + bx + c, a ¿ 1 

5.4 Factoring Squares of Binomials 

5.5 A General Factoring Strategy 

5.6 Solving Quadratic Equations by Factoring 

5.7 Applications of Quadratics 

6. Rational Expressions6.1 Building and Reducing Rational Expressions 

6.2 Multiplication and Division of Rational Expressions 

6.3 Addition and Subtraction of Rational Expressions 


6.5 Solving Equations Containing Rational Expressions 

6.6 Ration, Proportion, and Applications 

6.7 Direct and Inverse Variation: Applications 

7. Solving Systems of Linear Equations and Inequalities7.1 Solving 

Systems of Equations by Graphing 

7.2 Solving Systems of Equations by Substitution 

7.3 Solving Systems of Equations by elimination 

7.4 Coin, General, motion, and Investment Problems 

7.5 Systems of Linear Inequalities 

8. Roots and Radicals8.1 Finding Roots 

8.2 Multiplication and Division of Radicals 

8.3 Addition and Subtraction of Radicals 

8.4 Simplifying Radicals 

8.5 Applications: Solving Radical Equations 

9. Quadratic Equations9.1 Solving Quadratic Equations by the Square 

Root Property 

9.2 Solving Quadratic Equations by Completing the Square 

9.3 Solving Quadratic Equations by the Quadratic Formula 

9.4 Graphing Quadratic Equations 

9.5 The Pythagorean Theorem and Other Applications 

9.6 Functions 

NEW *9780073406169* 

BEGINNING ALGEBRA 

By Sherri Messersmith, College of Dupage 

2012 (January 2011) / 800 pages 

ISBN: 9780073406169 

www. mhhe.com/math/devmath/Messersmith_BIA/ 

Beginning Algebra, 1e, authored by Sherri Messersmith presents 

content in bite-size pieces, focusing not only on learning mathematical 

concepts, but also explaining the why behind those concepts. For 

students, learning mathematics is not just about the memorization of 

concepts and formulas, but it is also about the journey of learning 

how to problem solve. By breaking the sections down into manage- 

 

traditionally struggle, and then assists them in understanding that material 

to be successful moving forward. Proven pedagogical features, 

such as You Try problems after each example, reinforce a student’s 

mastery of a concept. While teaching in the classroom, Messersmith 

has created worksheets for each section that fall into three categories: 

review worksheets/basic skills, worksheets to teach new content, 

and worksheets to reinforce/pull together different concepts. These 

worksheets are a great way to both enhance instruction and to give 

the students more tools to be successful in studying a given topic. The 

 

 

it important to not only provide quality, but also an abundant quantity 

of exercises and applications. The book is accompanied by numerous 

useful supplements, including McGraw-Hill’s online homework 

management system, MathZone as well as ALEKS. 

MESSERSMITH is rigorous enough to prepare students for the next 

level yet easy to read and understand. The exposition is written as if 

a professor is teaching in a lecture to be more accessible to students. 

The language is mathematically sound yet easy enough for students 

to understand. 

FEATURES 

Several chapters contain a Putting It All Together section. In 

keeping with the author’s philosophy of breaking sections into manageable 

chunks, Messersmith includes this feature where needed 

to help the student to synthesize key topics before moving onto the 

rest of the chapter. 

MESSERSMITH provides worksheets for EVERY section of 

the textbook. These worksheets fall into three categories: review 

worksheets/basic skills, worksheets that teach new content, and worksheets 

to reinforce/pull together different concepts. These worksheets 

are a great way to both enhance instruction and to give students more 

tools to be successful in studying a given topic. They are ready-made 

materials for instructors! Perfect for adjuncts! Especially those who 

teach at more than one school and don’t have time to create tools 

for their classes. The worksheets help to standardize the level at 

which the course is taught. To help adjuncts keep pace with full-time 

instructors. *Available in MathZone and ALEKS. 

In order to give the instructors additional material to use in the 

classroom, a matching In-Class Example is provided in the margin 

of the AIE for every example in the book. 

 

“USING TECHNOLOGY” BOXES 

For those instructors who want to make use of graphing calculator-related 

material, Using Technology Boxes are included at the 

ends of sections where relevant. For those instructors who don’t want 

to use this material, they are easily skipped. 

The end-of-section exercise sets have been organized similarly 

to the examples—they are presented from the most basic to the most 

rigorous so that students may see how the concepts work at the 

simplest level before progressing to more difficult problems. Mixed 

exercise subsets are also provided where problems from multiple 

objectives within a section are solved. Messersmith has incorporated 

interesting real-world, up-to-date, relevant information that will appeal 

to students of all backgrounds into the applications in the book. 

Students have identified a number of the problems as interesting and 

fun in previous use. Within these exercises, students and faculty will 

find video, calculator, and writing exercise icons. 

The comprehensive Summaries at the end of each chapter enable 

students to review important concepts. A definition or concept is 

presented, along with a related example and a page reference from 

the relevant section. 

At the end of each chapter, you will find a set of Review Exercises, 

a Chapter Test, and a comprehensive Cumulative Review (starting 

with Chapter 2.) 

Chapter 1 includes a review of basic concepts from geometry. 

Throughout beginning and intermediate algebra courses, students 

need to know these basics, but many do not. Section 1.3 provides 

the material necessary for faculty to teach & students to practice the 

geometry concepts they will later in the course. The book also includes 

geometry applications where appropriate. 

12


After nearly every example, there is a “You Try” problem that 

mirrors that example. This provides students with the opportunity to 

practice a problem similar to what the instructor has presented before 

moving on to the next concept. Answers are provided at the end of 

the section for immediate feedback. 

Chapter-Opening Vignettes: Each chapter opens with a realworld 

vignette to capture the student’s attention and engage them 

in the upcoming material. The openers fall into five different themes 

for sake of consistency. 

Learning Objectives are clearly identified at the beginning of each 

section. The objectives then appear within the body of the text, showing 

when a particular objective is about to be developed. References 

are also included within the exercise sets to help students quickly 

reference related material if they need more practice. 

There are some mistakes that are very common for students to 

make. The “Be Careful!” boxes make students aware of these common 

errors so that, hopefully, they will not make these mistakes themselves. 

New Fill It In exercises take a student through the process of 

working out a problem step-by-step so that students have to provide 

the reason for each mathematical step to solve the problem, much 

like a geometry proof. 

New Guided Student Notes are an amazing resource for instructors 

to help their students become better note-takers. They contain 

in-class examples provided in the margin of the text along with additional 

examples not found in the book to emphasize the give topic 

so that students have less time copying down information and more 

time engaging within the classroom. 

CONTENTS 

Chapter 1 The Real Number System and Geometry 

1.1 Review of Fractions 

1.2 Exponents and Order of Operations 

1.3 Geometry Review 

1.4 Sets of Numbers and Absolute Value 

1.5 Addition and Subtraction of Real Numbers 

1.6 Multiplication and Division of Real Numbers 

1.7 Algebraic Expressions and Properties of Real Numbers 

Chapter 2 The Rules of Exponents 

2.1 Basic Rules of Exponents 

Part A The Product Rule and Power Rules 

Part B Combining the Rules 

2.2 Integer Exponents Bases 

Part A Real-Number Bases 

Part B Variable Bases 

2.3 The Quotient Rule 

Putting It All Together 


Chapter 3 Linear Equations and Inequalities 

3.1 Solving Linear Equations Part I 

3.2 Solving Linear Equations Part II 

3.3 Solving Linear Equations Part III 

3.4 Applications of Linear Equations 

3.5 Applications Involving Percentages 

3.6 Geometry Applications and Solving Formulas 

3.7 Applications of Linear Equations to Proportions, Money Problems, 

and d=rt 

3.8 Solving Linear Inequalities in One Variable 

Chapter 4 Linear Equations in Two Variables 

4.1 Introduction to Linear Equations in Two Variables 

4.2 Graphing by Plotting Points and Finding Intercepts 

4.3 The Slope of a Line 

4.4 The Slope-Intercept Form of a Line 

4.5 Writing an Equation of a Line 

4.6 Introduction to Functions 

Chapter 5 Solving Systems of Linear Equations 

5.1 Solving Systems by Graphing 

5.2 Solving Systems by Substitution 

5.3 Solving Systems by the Elimination Method 


5.4 Applications of Systems of Two Equations 

5.5 Linear Inequalities in Two Variables 

Chapter 6 Polynomials 

6.1 Review of the Rules of Exponents 

6.2 Addition and Subtraction of Polynomials; Graphing 



Chapter 7 Factoring Polynomials 

7.1 The Greatest Common Factor and Factoring by Grouping 

7.2 Factoring Trinomials of the Form x2+bx+c 

7.3 Factoring Trinomials of the Form ax2+bx+c (a¿1) 

7.4 Factoring Special Trinomials and Binomials 



7.6 Applications of Quadratic Equations 

Chapter 8 Rational Expressions 

8.1 Simplifying Rational Expressions 

8.2 Multiplying and Dividing Rational Expressions 

8.3 Finding the Least Common Denominator 

8.4 Adding and Subtracting Rational Expressions 


8.5 Simplifying Complex Fractions 

8.6 Solving Rational Equations 

8.7 Applications of Rational Equations and Variation 

Chapter 9 Radicals and Rational Exponents 

9.1 Finding Roots 

9.2 Simplifying Expressions Containing Radicals 

9.3 Adding and Subtracting Radicals 

9.4 Combining Operations on Radicals 

9.5 Dividing Radicals 

9.6 Solving Radical Equations 

9.7 Rational Exponents 

Chapter 10 Quadratic Equations 

10.1 Solving Quadratic Equations Using the Square Root Property 


10.3 Solving Quadratic Equations Using the Quadratic Formula 


10.4 Complex Numbers 

10.5 Graphs of Quadratic Equations 

Appendix 

A.1 Mean, Median, and Mode 

A.2 Systems of Linear Equations in Three Variables 

A.3 Quadratic Inequalities 

REVIEW COPY 

(Available for course adoption only) 

To request for a review copy, 

• contact your local McGraw-Hill 

representatives or, 

• fax the Review Copy Request Form found 

in this catalog or, 

• e-mail your request to 

mghasia_sg@mcgraw-hill.com or, 


13


NEW 

*9780077349936* 

BEGINNING ALGEBRA 

3rd Edition 

by Julie Miller, Molly O’Neill, and Nancy Hyde, 

Daytona State College 

2011 (January 2010) / Hardcover / 816 pages 

ISBN: 9780077349936 


 

tion, Beginning Algebra 3/e continues to offer an enlightened approach 

grounded in the fundamentals of classroom experience. The practice 

of many instructors in the classroom is to present examples and have 

their students solve similar problems. This is realized through the Skill 

Practice Exercises that directly follow the examples in the textbook. 

Throughout the text, the authors have integrated many Study Tips 

 

and instruction presented to students in the classroom. In this way, 

the text communicates to students, the very points their instructors 

are likely to make during lecture, helping to reinforce the concepts and 

provide instruction that leads students to mastery and success. The 

authors included in this edition, Problem-Recognition exercises, that 

many instructors will likely identify to be similar to worksheets they 

have personally developed for distribution to students. The intent of 

the Problem-Recognition exercises, is to help students overcome what 

is sometimes a natural inclination toward applying problem-solving 

algorithms that may not always be appropriate. In addition, the exercise 

sets have been revised to include even more core exercises 

than were present in the previous edition. This permits instructors to 

choose from a wealth of problems, allowing ample opportunity for 

students to practice what they learn in lecture to hone their skills and 

develop the knowledge they need to make a successful transition into 

Intermediate Algebra. In this way, the book perfectly complements any 

learning platform, whether traditional lecture or distance-learning; its 

 

will feel as comfortable outside of class, as they do inside class with 

their instructor. 

FEATURES 

NEW! Problem Recognition Exercises Developmental math 

students are sometimes conditioned into algorithmic thinking to the 

point where they want to automatically apply various algorithms to 

solve problems, whether it is meaningful or not. These exercises 

were built to decondition students from falling into that trap. Carefully 

crafted by the authors, the exercises focus on the situations where 

students most often get “mixed-up.” Working the Problem Recognition 

Exercises, students become conditioned to Stop, Think, and Recall 

what method is most appropriate to solve each problem in the set. 

Skill Practice exercises follow immediately after the examples in 

the text. Answers are provided so students can check their work. By 

utilizing these exercises, students can test their understanding of the 

various problem-solving techniques given in the examples. 

The section-ending Practice Exercises are newly revised, with 

even more core exercises appearing per exercise set. Many of the 

exercises are grouped by section objective, so students can refer 

back to content within the section if they need some assistance in 

completing homework. Review Problems appear at the beginning 

of most Practice Exercise Sets to help students improve their study 

habits and to improve their long-term retention of concepts previously 

introduced. 

Mixed Exercises are found in many of the Practice Exercise 

sets. The Mixed Exercises contain no references to objectives. 

In this way, students are expected to work independently without 

prompting --which is representative of how they would work through 

a test or exam. 

Study Skills Exercises appear at the beginning of the Practice 

Exercises, where appropriate. They are designed to help students 

learn techniques to improve their study habits including exam preparation, 

note taking, and time management. 

The Chapter Openers now include a variety of puzzles that may 

be used to motivate lecture. Each puzzle is based on key vocabulary 

terms or concepts that are introduced in the chapter. 

Classroom Activities are optional exercises that can be worked 

out in class by individual students, or a group of students who work 

collaboratively. The Annotated Instructor’s Edition refers to the classroom 

activities, which are found in the Instructor’s Resource Manual. 

Instructors have the option of making the classroom activities available 

to students for use in class in conjunction with lecture, or for use as 

extra practice in conjunction with homework. 

CONTENTS 

R Reference 

R.1 Study Tips 

R.2 Fractions 

R.3 Decimals and Percents 

R.4 Introduction to Geometry 

1 Set of Real Numbers 

1.1 Sets of Numbers and the Real Number Line 



1.4 Subtraction of Real Numbers 


1.6 Properties of Real Numbers and Simplifying Expressions 

2 Linear Equations and Inequalities 

2.1 Addition, Subtraction, Multiplication, and Division Properties of 

Equality 


2.3 Linear Equations: Clearing Fractions and Decimals 

2.4 Applications of Linear Equations: Introduction to Problem Solving 

2.5 Applications Involving Percents 

2.6 Formulas and Applications of Geometry 

2.7 Linear Inequalities 

3 Graphing Linear Equations in Two Variables 

3.1 Rectangular Coordinate System 


3.3 Slope of a Line 

3.4 Slope-Intercept Form of a Line 

3.5 Point-Slope Formula 


4 Systems of Linear Equations and Inequalities in Two Variables 

4.1 Solving Systems of Equations by the Graphing Method 

4.2 Solving Systems of Equations by the Substitution Method 

4.3 Solving Systems of Equations by the Addition Method 

4.4 Applications of Linear Equations in Two Variables 


4.6 Systems of Linear Inequalities in Two Variables 

5 Polynomials and Properties of Exponents 

5.1 Exponents: Multiplying and Dividing Common Bases 

5.2 More Properties of Exponents 

5.3 Definitions of b^0 and b^-n 





6 Factoring Polynomials 

6.1 Greatest Common Factor and Factoring by Grouping 

6.2 Factoring Trinomials of the Form x^2+ bx+ c(optional) 

6.3 Factoring Trinomials: Trial-and-Error Method 

6.4 Factoring Trinomials: AC-Method 

6.5 Factoring Binomials 

6.6 General Factoring Summary 

6.7 Solving Equations Using the Zero Product Rule 

7 Rational Expressions 

14


7.1 Introduction to Rational Expressions 


7.3 Least Common Denominator 



7.6 Rational Equations 

7.7 Applications of Rational Equations and Proportions 

7.8 Variations 

8 Radicals 

8.1 Introducion to Roots and Radicals 



8.4 Multiplication of Radicals 

8.5 Rationalization 

8.6 Radical Equations 


9 Functions, Complex Numbers, and Quadratic Equations 



9.3 The Square Root Property and Completing the Square 

9.4 Quadratic Formula 

9.5 Graphing Quadratic Functions 

HUTCHINSON’S BEGINNING ALGEBRA 

8th Edition 

By Stefan Baratto, Barry Bergman, and Donald Hutchison, all of Clackamas 


2010 (November 2009) / Softcover / 896 pages 

ISBN: 9780077354756 


Put the content in context! Continuing its hallmark approach of mastering 

math through practice, this worktext provides carefully detailed 

explanations and accessible pedagogy to introduce basic algebra 

skills. The material is presented in a three pronged approach: communication, 

pattern recognition, and problem solving. 

CONTENTS 

1 The Language of Algebra 

1.1 Properties of Real Numbers 



1.4 From Arithmetic to Algebra 


1.6 Adding and Subtracting Terms 

1.7 Multiplying and Dividing Terms 

2 Equations and Inequalities 

2.1 Solving Equations by the Addition Property 

2.2 Solving Equations by the Multiplication Property 

2.3 Combining the Rules to Solve Equations 

2.4 Formulas and Problem Solving 


2.6 Inequalities--An Introduction 

3 Polynomials 

3.1 Exponents and Polynomials 

3.2 Negative Exponents and Scientific Notation 

3.3 Adding and Subtracting Polynomials 


3.5 Dividing Polynomials 

4 Factoring 

4.1 An Introduction to Factoring 

4.2 Factoring Trinomials of the Form x2 + bx + c 

4.3 Factoring Trinomials of the Form ax2 + bx + c 

4.4 Difference of Squares and Perfect Square Trinomials 

4.5 Strategies in Factoring 





5.3 Adding and Subtracting Like Rational Expressions 

5.4 Adding and Subtracting Unlike Rational Expressions 

5.5 Complex Rational Expressions 

5.6 Equations Involving Rational Expressions 

5.7 Applications of Rational Expressions 

6 An Introduction to Graphing 

6.1 Solutions of Equations in Two Variables 


6.3 Graphing Linear Equations 


6.5 Reading Graphs 

7 Graphing and Inequalities 

7.1 The Slope-Intercept Form 

7.2 Parallel and Perpendicular Lines 

7.3 The Point-Slope Form 

7.4 Graphing Linear Inequalities 

7.5 An Introduction to Functions 

8 Systems of Linear Equations 

8.1 Systems of Linear Equations: Solving by Graphing 

8.2 Systems of Linear Equations: Solving by the Addition Method 

8.3 Systems of Linear Equations: Solving by Substitution 


9 Exponents and Radicals 

9.1 Roots and Radicals 

9.2 Simplifying Radical Expressions 

9.3 Adding and Subtracting Radicals 

9.4 Multiplying and Dividing Radicals 

9.5 Solve Radical Equations 

9.6 Applications of the Pythagorean Theorem 

10 Quadratic Equations 

10.1 More on Quadratic Equations 

10.2 Completing the Square 

10.3 The Quadratic Formula 

10.4 Graphing Quadratic Equations 

INTRODUCTORY ALGEBRA 

2nd Edition 



2009 (November 2008) / 832 pages 

ISBN: 9780077281120 

ISBN: 9780077303877 [Hardcover] 


Introductory Algebra offers a refreshing approach to the traditional 

content of the course. Presented in worktext format, Introductory 

Algebra focuses on solving equations and inequalities, graphing, 

polynomials, factoring, rational expressions, and radicals. Other topics 

include quadratic equations and an introduction to functions and 

 

its experienced author team with features developed to address the 

 

CONTENTS 

Chapter 1: The Set of Real Numbers 




1.4 Subtraction of Real Numbers--Problem Recognition Exercises— 

Addition and Subtraction of Signed Numbers 



Chapter 2: Linear Equations and Inequalities 


Equality 


2.3 Linear Equations: Clearing Fractions and Decimals--Problem 

Recognition Exercises—Equations and Expressions 

15





2.7 Mixture Applications and Uniform Motion 


Chapter 3: Graphing Linear Equations in Two Variables 




3.4 Slope-Intercept Form of a Line--Problem Recognition Exercises— 

Linear Equations in Two Variables 




Chapter 4: Systems of Linear Equations in Two Variables 



4.3 Solving Systems of Equations by the Addition Method--Problem 

Recognition Exercises—Systems of Equations 

4.4 Applications of Linear Equations in Two Variables 4.5 Linear 

Inequalities and Systems of Inequalities in Two Variables 

Chapter 5: Polynomials and Properties of Exponents 



5.3 Definitions of and 

5.4 Scientific Notation--Problem Recognition Exercises—Properties 

of Exponents 



5.7 Division of Polynomials--Problem Recognition Exercises—Operations 

on Polynomials 

Chapter 6: Factoring Polynomials 


6.2 Factoring Trinomials of the Form 



6.5 Factoring Special Patterns 

6.6 Sum and Difference of Cubes--Problem Recognition Exercises— 

General Factoring Strategy 

6.7 Solving Equations Using the Zero Product Rule--Problem Recognition 

Exercises—Expressions and Polynomial Equations 


Chapter 7: Rational Expressions 




7.4 Addition and Subtraction of Rational Expressions--Problem Recognition 

Exercises—Operations on Rational Expressions 


7.6 Rational Equations--Problem Recognition Exercises—Comparing 

Rational Equations and Rational Expressions 


7.8 Variation 

Chapter 8: Radicals 

8.1 Introduction to Roots and Radicals 




8.5 Division of Radicals and Rationalization--Problem Recognition 

Exercises—Operations on Radicals 



Chapter 9: More Quadratic Equations 

9.1 The Square Root Property 


9.3 Quadratic Formula--Problem Recognition Exercises—Solving 

Quadratic Equations 


ELEMENTARY ALGEBRA 

6th Edition 

By Mark Dugopolski 

2009 (January 2008) / 704 pages 

ISBN: 9780077224790 

www.mhhe.com/dugopolski 

Elementary Algebra, 6e is part of the latest offerings in the successful 

Dugopolski series in mathematics. The author’s goal is to explain 

mathematical concepts to students in a language they can understand. 

 

of terms and concepts written in understandable language. The 

author uses concrete analogies to relate math to everyday experiences. 

For example, when the author introduces the Commutative 

Property of Addition, he uses a concrete analogy that “the price of a 

hamburger plus a Coke is the same as a Coke plus a hamburger”. 

Given the importance of examples within a math book, the author 

has paid close attention to the most important details for solving the 

given topic. Dugopolski includes a double cross-referencing system 

between the examples and exercise sets, so no matter which one the 

students start with, they will see the connection to the other. Finally, 

 

good quantity of exercises and applications. The Dugopolski series 

is known for providing students and faculty with the most quantity 

and quality of exercises as compared to any other developmental 

math series on the market. In completing this revision, Dugopolski 

feels he has developed the clearest and most concise developmental 

math series on the market, and he has done so without comprising 

the essential information every student needs to become successful 

in future mathematics courses. The book is accompanied by numerous 


management system, MathZone. 

CONTENTS 

TO THE STUDENT 

PREFACE 

1 Real Numbers and Their Properties 


1.2 Fractions 



1.5 Exponential Expressions and the Order of Operations 

1.6 Algebraic Expressions 


1.8 Using the Properties to Simplify Expressions 

Chapter 1 Wrap-Up 

 

 

 

 

 

2 Linear Equations and Inequalities in One Variable 2 

.1 The Addition and Multiplication Properties of Equality 

2.2 Solving General Linear Equations 

2.3 More Equations 

2.4 Formulas 

2.5 Translating Verbal Expressions into Algebraic Expressions 

2.6 Number, Geometric, and Uniform Motion Applications 

2.7 Discount, Investment, and Mixture Applications 

2.8 Inequalities 

2.9 Solving Inequalities and Applications 


 

 

 

 

 

 

3 Linear Equations in Two Variables and Their Graphs 

3.1 Graphing Lines in the Coordinate Plane 

3.2 Slope 

3.3 Equations of Lines in Slope-Intercept Form 


16




 

 

 

 

 

 

4 Systems of Linear Equations and Inequalities 

4.1 The Graphing Method 

4.2 The Substitution Method 

4.3 The Addition Method 

4.4 Graphing Linear Inequalities in Two Variables 

4.5 Graphing Systems of Linear Inequalities 


 

 

 

 

 

 

5 Exponents and Polynomials 

5.1 The Rules of Exponents 




5.5 Multiplication of Binomials 

5.6 Special Products 



 

 

 

 

 

 

6 Factoring 

6.1 Factoring Out Common Factors 

6.2 Special Products and Grouping 

6.3 Factoring the Trinomial ax² + bx + c with a = 1 

6.4 Factoring the Trinomial ax² + bx + c with a ¿ 1 

6.5 The Factoring Strategy 



 

 

 

 

 

 


7.1 Reducing Rational Expressions 

7.2 Multiplication and Division 


7.4 Addition and Subtraction 


7.6 Solving Equations with Rational Expressions 

7.7 Applications of Ratios and Proportions 



 

 

 

 

 

 

8 Powers and Roots 

8.1 Roots, Radicals, and Rules 

8.2 Simplifying Square Roots 

8.3 Operations with Radicals 

8.4 Solving Equations with Radicals and Exponents 

8.5 Fractional Exponents 


 

 

 

 

 

 

9 Quadratic Equations, Parabolas, and Functions 

9.1 The Square Root Property and Factoring 





9.6 Graphing Parabolas 


9.8 Combining Functions 


 

 

 

 

 

 

Appendix A: Geometry Review Exercises 

Appendix B: Sets 

Appendix C: Final Exam Review Answers to Selected Exercises Index 

SCHAUM’S OUTLINE OF ELEMENTARY 

ALGEBRA 

3rd Edition 

By Barnett Rich (deceased); Philip Schmidt, State University College— 

New Paltz 

2009 (May 2009) / 384 pages 

ISBN: 9780071611633 


 

in how the discipline is taught and introduces a new perspective on 

the discipline. New material in this third edition includes: 

 

 

 

 

 

A modernized section on trigonometry 

An introduction to mathematical modeling 

Instruction in use of the graphing calculator 

2,000 solved problems 

3,000 supplementary practice problems and more 

CONTENTS 

1. From Arithmetic to Algebra 

2. Simple Equations and Their Solutions 

3. Signed Numbers 

4. Introduction to Monomials and Polynomials 

5. First-Degree Equations 

6. Formulas 

7. Graphs of Linear Equations 

8. Introduction to Simultaneous Equations 

9. Problem Solving and Mathematical Modeling 

10. Products and Factoring 

11. Fractions 

12. Roots and Radicals 

13. Quadratic Equations 

14. The Pythagorean Theorem and Similar Triangles 

15. Introduction to Trigonometry 

16. Introduction to Geometry 

17



BOB MILLER’S ALGEBRA FOR THE 

CLUELESS 

2nd Edition 

By Bob Miller 

2007 / 240 pages 

ISBN: 9780071473668 


CONTENTS 

TO THE STUDENT 

Chapter 1: Natural Numbers and Introductory Terms 

Chapter 2: Integers Plus More 

Chapter 3: First-Degree Equations 

Chapter 4: Problems with Words: Why So Many Students Have 

Problems on the SAT 

Chapter 5: Factoring 

Chapter 6: Algebraic Fractions 

Chapter 7: Radicals and Exponents 

Chapter 8: Quadratics 

Chapter 9: Points, Lines, and Planes 

Chapter 10: Odds and Ends 

Chapter 11: Miscellaneous Miscellany 

APPENDIX 1: FRACTIONS, DECIMALS, PERCENTS, AND GRAPHS 

APPENDIX 2: SETS 

ACKNOWLEDGMENTS 

ABOUT BOB MILLER: IN HIS OWN WORDS 

INDEX 


2nd Edition 


2005 / 400 pages 

ISBN: 9780071435338 


CONTENTS 



2. Integers 


4. Fractions 




8. Graphing 










2004 / 308 pages 

ISBN: 9780071443166 


CONTENTS 

Preface 







QUIZ 1 





QUIZ 2 






QUIZ 3 







QUIZ 4 






QUIZ 5 




QUIZ 6 

FINAL EXAM 



INDEX 




2002 / 304 pages 

ISBN: 9780071376938 














18







MATHEMATICS 


2001 / 164 pages 

ISBN: 9780071362726 


CONTENTS 








TEST YOURSELF: ELEMENTARY ALGEBRA 

By Lawrence Trivieri, Georgia Permimeter College-Clarkston 

1996 / 176 pages 

ISBN: 9780844223568 


(Details unavailable at press time) 

Beginning/Intermediate 

Algebra Combined 

NEW *9780073384351* 

ELEMENTARY AND 

INTERMEDIATE ALGEBRA 

4th Edition 


2012 (January 2011) / 1056 pages 

ISBN: 9780073384351 

www.mhhe.com/math/devmath/dugopolski/ 

Elementary & Intermediate Algebra, 4e is part of the latest offerings 

in the successful Dugopolski series in mathematics. The author’s 

goal is to explain mathematical concepts to students in a language 

 

precise explanations of terms and concepts written in understandable 

language. The author uses concrete analogies to relate math 

to everyday experiences. For example, when the author introduces 

the Commutative Property of Addition, he uses a concrete analogy 

that “the price of a hamburger plus a Coke is the same as a Coke 

plus a hamburger”. Given the importance of examples within a math 

book, the author has paid close attention to the most important details 

for solving the given topic. Dugopolski includes a double crossreferencing 

system between the examples and exercise sets, so no 

matter which one the students start with, they will see the connection 

 

quality, but also a good quantity of exercises and applications. The 

Dugopolski series is known for providing students and faculty with 

the most quantity and quality of exercises as compared to any other 

developmental math series on the market. In completing this revision, 

Dugopolski feels he has developed the clearest and most concise 

developmental math series on the market, and he has done so without 

comprising the essential information every student needs to become 

successful in future mathematics courses. The book is accompanied 

by numerous useful supplements, including McGraw-Hill’s online 

homework management system, MathZone. 


Warm-up Exercises are ten simple true or false questions located at 

the end of every section. These exercises are designed to provide a 

smooth transition between the concepts in the section and the exercise 

sets. Helping your students recognize that many ideas in mathematics 

are either true or false can assist them in developing a broader 

 

in class discussions or group work. 

FEATURES 

The Strategy Boxes provide an eye-catching and useful reference 

for students when they are reviewing key concepts and solving 

techniques in order to prepare for tests and homework. They are 

directly referenced in the end-of-section exercises where appropriate. 

Examples refer directly to a set of exercises, and that set of 

exercises refers right back to those examples. This double crossreferencing 

allows students to make the connection between an 

example and a related exercise while in turn helping them to see how 

a worked out solution for one problem can lead them to finding their 

own solution for a similar problem. 

An emphasis on real-data applications involving graphs is a focus 

of the text. Some exercises have been updated throughout the text to 

help demonstrate concepts, motivate students, and to give students 

practice using new skills. Many of the real data exercises contain data 

obtained from the Internet. An Index of Applications listing applications 

by subject matter is included at the front of the text. 

Geometry Review Exercises - Located in the appendix, this 

review section can be used to assist students to remediate their 

Geometry skills learned in earlier courses. 

Chapter Openers feature real-world applications corresponding 

to relevant chapter topics. The discussion is accompanied by 

a photograph and, in most cases, by a real-data graph. This visual 

representation of algebra allows students to have a richer understanding 

of concepts discussed in each chapter. The chapter opener 

links the application to a related real data exercise that students may 

work through. 

The Math at Work feature appears in each chapter to reinforce the 

book’s theme of real applications in the everyday world. The feature 

profiles a real person and the mathematics that he or she uses on 

the job. Showing a student how math can be used in a variety of jobs 

promotes interest in the subject matter, and motivation for learning. 

In This Section is a list providing a preview of the topics to be 

covered in the section. These subsections are numbered for easy 

reference and, in addition, are placed by the appropriately linked 

end-of-section exercises. 

19


Important ideas, such as definitions, rules, summaries, and 

strategies, are set apart in boxes for quick reference. Color is used 

to highlight these boxes as well as other important points in the text. 

Margin Notes: Margin Notes are provided to assist students in 

various ways. 

Calculator Close-Ups This feature gives your students an idea of 

how and when to use a graphing calculator. Some Calculator Close- 

Ups simply introduce the features of a graphing calculator, where 

others enhance understanding of algebraic concepts. For this reason, 

many of the Calculator Close-Ups will benefit even those students 

who do not use a graphing calculator. 

Study Tips - Two study tips now precede every exercise set. They 

give the student information on best practices for studying, learning, 

and performing well academically. 

Helpful Hints are succinct explanations adjacently located to a 

topic. They enhance the chapter material by providing another way 

of approaching a problem, or clearing up misconceptions. 

Linked to the end of section exercises, students are guided from 

the examples within a section to the end of section exercises where 

they can master the given topic being studied. 

The Reading and Writing Exercises are designed to get your 

students to review the definitions and rules of the section before doing 

any traditional skill building sets. These can be used for class discussion 

and to verify students’ conceptual understanding of the subject 

matter while enhancing their ability to articulate mathematical ideas. 

Getting More Involved concludes the exercise set with Discussion, 

Writing, Exploration, and Cooperative Learning activities for 

well-rounded practice in the skills for that section. 

End-of-Section Exercises follow the same order as the textual 

material and contain exercises that are keyed to examples, as well as 

numerous exercises that are not keyed to examples. This organization 

allows the instructor to cover only part of a section if necessary 

and easily determine which exercises are appropriate to assign. The 

keyed exercises give your student a place to start practicing and 

building confidence, whereas the non-keyed exercises are designed 

to wean your student from following examples in a step-by-step manner. 

The exercise sets supply a generous and varied amount of drill 

and realistic applications so students can put into practice the skills 

they have developed. 

The Wrap-up is an extensive and varied review, located at the 

end of each chapter, available to help students prepare for exams. 

The Wrap-up includes the following: Summary is a list of important 

concepts along with brief illustrative examples of each. Enriching 

Your Mathematical Word Power enables students to test their recall 

of new terminology in a multiple-choice format. Review Exercises 

contain problems that are linked to the exact chapter and section the 

concept originally appears as well as a miscellaneous section with a 

mixed set of problems with no chapter or section links. The Chapter 

Test is designed to help your student ensure his or her preparedness 

and success for an upcoming exam. The Chapter Test does not have 

linked exercises, thus enabling the student to work independently 

of the sections and examples. All answers to the Chapter Test are 

provided at the back of the book and all worked out solutions are 

provided in the Student Solutions Manual. 

Following the Chapter Test is the Making Connections feature. 

It is a cumulative review of all chapters up to and including the one 

just completed. This feature helps tie course concepts together for 

students on a regular basis, while also reinforcing earlier learned 

material. Every Making Connections exercise set includes at least 

one applied exercise that requires ideas from one or more of the 

previous chapters. 

Optional calculator exercises appear throughout the exercise 

sets, providing students with the opportunity to use scientific or graphing 

calculators to solve various problem types. 

Video icons appear within the exercise sets indicating there is a 

video available to walk a student through the solution steps. 

CONTENTS 

PREFACE 

APPLICATIONS INDEX 

1 Real Numbers and Their Properties 


1.2 Fractions 



1.5 Exponential Expressions and the Order of Operations 



1.8 Using the Properties to Simplify Expressions 

2 Linear Equations and Inequalities in One Variable 

2.1 The Addition and Multiplication Properties of Equality 

2.2 Solving General Linear Equations 

2.3 More Equations 

2.4 Formulas and Functions 

2.5 Translating Verbal Expressions into Algebraic Expressions 

2.6 Number, Geometric, and Uniform Motion Applications 

2.7 Discount, Investment, and Mixture Applications 


2.9 Solving Inequalities and Applications 

3 Linear Equations and Inequalities in Two Variables 


3.2 Slope 

3.3 Equations of Lines in Slope-Intercept Form 






4.2 Negative Exponents 




4.6 Multiplication of Binomials 

4.7 Special Products 


5 Factoring 

5.1 Factoring Out Common Factors 

5.2 Special Products and Grouping 

5.3 Factoring the Trinomial ax² + bx + c with a = 1 

5.4 Factoring the Trinomial ax² + bx + c with a ¿ 1 

5.5 Difference and Sum of Cube and a Strategy 



6.1 Reducing Rational Expressions 





6.6 Solving Equations with Rational Expressions 

6.7 Applications of Ratios and Proportions 



7.1 The Graphing Method 

7.2 The Substitution Method 


7.4 Systems of Linear Equations in Three Variables 

8 More on Inequalities 

8.1 Compound Inequalities in One Variable 

8.2 Absolute Value Equations and Inequalities 

8.3 Compound Inequalities in Two Variables 

8.4 Linear Programming 

9 Radicals and Rational Exponents 

9.1 Radicals 


9.3 Adding, Subtracting, and Multiplying Radicals 

20


9.4 Quotients, Powers, and Rationalizing Denominators 



10 Quadratic Equations and Inequalities 

10.1 Factoring and Completing the Square 




10.5 Quadratic Inequalities 

11 Functions 

11.1 Functions and Relations 

11.2 Graphs of Functions and Relations 

11.3 Transformations of Graphs 

11.4 Graphs of Polynomial Functions 

11.5 Graphs of Rational Functions 


11.7 Inverse Functions 

12 Exponential and Logarithmic Functions 

12.1 Exponential Functions and Their Applications 

12.2 Logarithmic Functions and Their Applications 

12.3 Properties of Logarithms 

12.4 Solving Equations and Applications 

13 Nonlinear Systems and the Conic Sections 

13.1 Nonlinear Systems of Equations 

13.2 The Parabola 

13.3 The Circle 

13.4 The Ellipse and Hyperbola 

13.5 Second-Degree Inequalities 

14 Sequences and Series (Available online at www.mhhe.com/ 

dugopolski) 

14.1 Sequences 

14.2 Series 

14.3 Arithmetic Sequences and Series 

14.4 Geometric Sequences and Series 

14.5 Binomial Expansions 

Appendix A: Geometry Review Exercises 

Appendix B: Sets 

Appendix C: Chapters 1-6 Diagnostic Test 

Appendix D: Chapters 1-6 Review 

Answers to Selected Exercises 

Index 

NEW 

*9780073384375* 

BEGINNING AND 


3rd Edition 

By Sherri Messersmith, College of Dupdge 

2012 (January 2011) / 1024 pages 

ISBN: 9780073384375 

www.mhhe.com/math/devmath/Messersmith_BIA/ 

Beginning and Intermediate Algebra, 3e, authored by Sherri Messersmith 

presents content in bite-size pieces, focusing not only on 

learning mathematical concepts, but also explaining the why behind 

those concepts. For students, learning mathematics is not just about 

the memorization of concepts and formulas, but it is also about the 

journey of learning how to problem solve. By breaking the sections 

 

places where students traditionally struggle, and then assists them in 

understanding that material to be successful moving forward. Proven 

pedagogical features, such as You Try problems after each example, 

reinforce a student’s mastery of a concept. While teaching in the classroom, 

Messersmith has created worksheets for each section that fall 

into three categories: review worksheets/basic skills, worksheets to 

teach new content, and worksheets to reinforce/pull together different 

concepts. These worksheets are a great way to both enhance instruction 

and to give the students more tools to be successful in studying 

a given topic. The author is also an extremely popular lecturer, and 

 

 

an abundant quantity of exercises and applications. The book is accompanied 

by numerous useful supplements, including McGraw-Hill’s 

online homework management system, MathZone as well as ALEKS. 







Fill-it-in Exercises take a student through the process of working 

out a problem step-by-step so that students have to provide the 

reason for each mathematical step to solve the problem, much like 

a geometry proof. 

FEATURES 

Putting It All Together: Several chapters contain a Putting It All 

Together section. In keeping with the author’s philosophy of breaking 

sections into manageable chunks, Messersmith includes this feature 

where needed to help the student to synthesize key topics before 

moving onto the rest of the chapter. 

WORKSHEETS: MESSERSMITH provides worksheets for 

EVERY section of the textbook. These worksheets fall into three 

categories: review worksheets/basic skills, worksheets that teach new 

content, and worksheets to reinforce/pull together different concepts. 

These worksheets are a great way to both enhance instruction and to 

give students more tools to be successful in studying a given topic. 

They are ready-made materials for instructors! Perfect for adjuncts! 

Especially those who teach at more than one school and don’t have 

time to create tools for their classes. 

The worksheets help to standardize the level at which the course 

is taught. To help adjuncts keep pace with full-time instructors. 

 

*Available in MathZone and ALEKS. 

In-Class Examples: In order to give the instructors additional 

material to use in the classroom, a matching In-Class Example is 

provided in the margin of the AIE for every example in the book. 

You Try Problems: After nearly every example, there is a “You 

Try” problem that mirrors that example. This provides students with 

the opportunity to practice a problem similar to what the instructor 

has presented before moving on to the next concept. Answers are 

provided at the end of the section for immediate feedback. 










Be Careful Boxes: There are some mistakes that are very common 

for students to make. The “Be Careful!” boxes make students 

aware of these common errors so that, hopefully, they will not make 

these mistakes themselves. 

Using Technology Boxes: For those instructors who want to 

make use of graphing calculator-related material, Using Technology 

Boxes are included at the ends of sections where relevant. For those 

instructors who don’t want to use this material, they are easily skipped. 

21


End-of-Section Exercises: The end-of-section exercise sets have 

been organized similarly to the examples—they are presented from 

the most basic to the most rigorous so that students may see how the 

concepts work at the simplest level before progressing to more difficult 

problems. Mixed exercise subsets are also provided where problems 

from multiple objectives within a section are solved. Messersmith has 

incorporated interesting real-world, up-to-date, relevant information 

that will appeal to students of all backgrounds into the applications 

in the book. Students have identified a number of the problems as 

interesting and fun in previous use. Within these exercises, students 

and faculty will find video, calculator, and writing exercise icons. 

Chapter Summary: The comprehensive Summaries at the end 

of each chapter enable students to review important concepts. A 

definition or concept is presented, along with a related example and 

a page reference from the relevant section. 

End-of-Chapter Material: At the end of each chapter, you will 

find a set of Review Exercises, a Chapter Test, and a comprehensive 

Cumulative Review (starting with Chapter 2.) 

Geometry Review: Chapter 1 includes a review of basic concepts 

from geometry. Throughout beginning and intermediate algebra 

courses, students need to know these basics, but many do not. Section 

1.3 provides the material necessary for faculty to teach & students 

to practice the geometry concepts they will later in the course. The 

book also includes geometry applications where appropriate. 

Beginning Algebra Review Appendix: Also as a result of reviewer 

feedback, Messersmith has now included a Beginning Algebra review 

in an appendix to bridge the gap to Intermediate Algebra for those 

who need it. It is included as an Appendix so that the instructor can 

use it where best fits their curriculum. 

CONTENTS 

1 The Real Number System and Geometry 

1.1 Review of Fractions 

1.2 Exponents and Order of Operations 

1.3 Geometry Review 

1.4 Sets of Numbers and Absolute Value 




2 The Rules of Exponents 

2.1 Basic Rules of Exponents 

Part A The Product Rule and Power Rules 

Part B Combining the Rules 

2.2 Integer Exponents 

Part A Real-Number Bases 

Part B Variable Bases 

2.3 The Quotient Rule 




3.1 Solving Linear Equations Part I 

3.2 Solving Linear Equations Part II 


3.4 Applications Involving Percentages 


3.6 Applications of Linear Equations to Proportions, Money Problems, 

and d=rt 

3.7 Solving Linear Inequalities in One Variable 

3.8 Solving Compound Inequalities 

4 Linear Equations in Two Variables 


4.2 Graphing by Plotting Points and Finding Intercepts 


4.4 The Slope-Intercept Form of a Line 



5 Solving Systems of Linear Equations 

5.1 Solving Systems by Graphing 

5.2 Solving Systems by Substitution 

5.3 Solving Systems by the Elimination Method 


5.4 Applications of Systems of Two Equations 

5.5 Systems of Three Equations and Applications 

6 Polynomials 

6.1 Review of the Rules of Exponents 






7.2 Factoring Trinomials of the Form x2+bx+c 

7.3 Factoring Trinomials of the Form ax2+bx+c (a¿1) 

7.4 Factoring Special Trinomials and Binomials 












8.7 Applications of Rational Equations 

9 More Equations and Inequalities 

9.1 Solving Absolute Value Equations 

9.2 Solving Absolute Value Inequalities 

9.3 Solving Linear and Compound Linear Inequalities in Two Variables 

9.4 Solving Systems of Linear Equations Using Matrices 


10.1 Finding Roots 


10.3 Simplifying Expressions Containing Square Roots 

10.4 Simplifying Expressions Containing Higher Roots 






11 Quadratic Equations 

11.1 Review of Solving Equations by Factoring 




11.6 Equations in Quadratic Form 

11.7 Formulas and Applications 

12 Functions and their Graphs 

12.1 Relations and Functions 

12.2 Graphs of Functions and Transformations 

12.3 Quadratic Functions and Their Graphs 

12.4 Applications of Quadratic Functions and Graphing Other Parabolas 

12.5 The Algebra of Functions 

12.6 Variation 

13 Exponential, and Logarithmic Functions 


13.2 Exponential Functions 

13.3 Logarithmic Functions 


13.5 Common and Natural Logarithms and Change of Base 

13.6 Solving Exponential and Logarithmic Equations 

14 Conic Sections, Nonlinear Inequalities, and Nonlinear Systems 


14.2 The Ellipse and the Hyperbola 



14.4 Quadratic and Rational Inequalities 

15 Sequences and Series (Online Only) 

15.1 Sequences and Series 

22




15.4 The Binomial Theorem 

A Appendix: Beginning Algebra Review 

A1 The Real Number System and Geometry 

A2 Variables and Exponents 

A3 Linear Equations and Inequalities 

A4 Linear Equations in Two Variables and Functions 

A5 Solving Systems of Linear Equations 

A6 Polynomials 

A7 Factoring Polynomials 

A8 Rational Expressions 

NEW *9780077350123* 

HUTCHINSON’S ELEMENTARY 

AND INTERMEDIATE ALGEBRA 

4th Edition 

By Stefan Baratto, Barry Bergman, and Donald 

Hutchison, all of Clackamas Community College 


ISBN: 9780077350123 


Elementary & Intermediate Algebra, 4/e by Baratto/Bergman is part 

of the latest offerings in the successful Streeter-Hutchison Series in 

Mathematics. The fourth edition continues the hallmark approach of 

encouraging the learning of mathematics by focusing its coverage 

on mastering math through practice. This worktext seeks to provide 

carefully detailed explanations and accessible pedagogy to introduce 

beginning and intermediate algebra concepts and put the content in 

context. The authors use a three-pronged approach (I. Communication, 

II. Pattern Recognition, and III. Problem Solving) to present the 

material and stimulate critical thinking skills. Items such as Math 

Anxiety boxes, Check Yourself exercises, and Activities represent 

this approach and the underlying philosophy of mastering math 

through practice. The exercise sets have been expanded, organized, 

and clearly labeled. Vocational and professional-technical exercises 

have been added throughout. Repeated exposure to this consistent 

structure should help advance the student’s skills in relating to 

mathematics. The book is designed for a combined beginning and 

intermediate algebra course, or it can be used across two courses, 

and is appropriate for lecture, learning center, laboratory, or self-paced 

courses. It is accompanied by numerous useful supplements, including 

McGraw-Hill’s online homework management system, MathZone. 

FEATURES 

MID-TEXT REVIEW CHAPTER -- The Review Chapter provides 

a concise, comprehensive review of chapters 1 through 6. The chapter 

contains review exercises and section references. 

“MAKE THE CONNECTION” --Chapter-Opening Vignettes 

were substantially revised to provide students interesting, relevant 

scenarios that will capture their attention and engage them in the 

upcoming material. Furthermore, exercises and Activities related to 

the Opening Vignettes were added or updated in each chapter. These 

exercises are marked with a special icon next to them. 

ACTIVITIES -- An Activity is included in each chapter. These 

Activities promote active learning by requiring students to find, interpret, 

and manipulate real-world data. The Activity in each chapter 

relates to the chapter-opening vignette, providing cohesiveness to 

the chapter. Students can complete the Activities on their own, but 

are best solved in small groups. 

CHECK YOURSELF EXERCISES -- Check Yourself exercises 

have been the hallmark of the Streeter-Hutchison Series; they are 

designed to actively involve students throughout the learning process. 

Each example is followed by an exercise that encourages students to 

solve a problem similar to the one just presented and check/practice 

what they have just learned. Answers to these exercises are provided 

at the end of the section for immediate feedback. 

“READING YOUR TEXT” -- This new feature is a set of quick 

exercises presented at the end of each section meant to quiz students 

vocabulary knowledge. These exercises are designed to encourage 

careful reading of the text. Answers to these exercises are provided 

at the end of the book. 

RESTRUCTURING OF END-OF-SECTION EXERCISES -- The 

comprehensive End-of-Section exercises have been reorganized to 

more clearly identify the different types of exercises being presented. 

This structure highlights the progression in level and type of exercise 

for each section. The application exercises that are now integrated 

into every section are a crucial component of this organization. 

SUMMARY AND SUMMARY EXERCISES -- The comprehensive 

chapter summaries and exercises are found at the end of every 

chapter and review the important concepts from that chapter. The 

comprehensive Summaries at the end of each chapter enable students 

to review important concepts. The Summary Exercises provide an opportunity 

for the student to practice these important concepts. Answers 

to odd-numbered exercises are provided in the Answers Appendix. 

CUMULATIVE REVIEWS -- Cumulative Reviews are included 

starting with Chapter 2, following the Self-Tests. These reviews help 

students build on previously covered material and give them an opportunity 

to reinforce the skills necessary in preparing for midterm 

and final exams. The answers to these exercises are also given at 

the end of the book, along with section references. 

OVERCOMING MATH ANXIETY -- Located within the first few 

chapters, these suggestions are designed to be timely and useful. 

They are similar to many of the same suggestions most instructors 

make in class, but having them in print provides another opportunity 

to impact the student. 

GRAPH PAPER INCLUDED -- A graph paper card is bound into 

the back of the book. This perforated card can be torn out and copied 

as needed by the students, and can be used any time they need to 

do graphing. An electronic version of the card is available through 

the book’s website in the Information Center. 

CONTENTS 

0 Prealgebra Review 

0.1 A Review of Fractions 

0.2 Real Numbers 



0.5 Exponents and Order of Operation 

1 From Arithmetic to Algebra 

1.1 Transition to Algebra 



1.4 Sets 

2 Functions and Graphs 

2.1 Solving Equations by Adding and Subtracting 

2.2 Solving Equations by Multiplying and Dividing 


2.4 Literal Equations and Their Applications 

2.5 Solving Linear Inequalities Using Addition 

2.6 Solving Linear Inequalities Using Multiplication 

2.7 Solving Absolute Value Equations (Optional) 

2.8 Solving Absolute Value Inequalities (Optional) 

3 Graphing Linear Functions 


3.2 The Cartesian Coordinate System 

3.3 The Graph of a Linear Equation 


23


3.5 Forms of Linear Equations 



4.1 Positive Integer Exponents 

4.2 Zero and Negative Exponents and Scientific Notation 



4.5 Multiplication of Polynomials and Special Products 




5.2 Factoring Special Polynomials 

5.3* Factoring Trinomials: Trial and Error 

5.4 Factoring Trinomials: The ac method 



5.7 Problem Solving with Factoring 

R A Review of Elementary Algebra 

R.1 From Arithmetic to Algebra 

R.2 Equations and Inequalities 

R.3 Graphs and Linear Equations 

R.4 Exponents and Polynomials 

R.5 A Beginning Look at Functions 

R.6 Factoring Polynomials 



6.2 Tables and Graphs 

6.3 Algebra of Functions 

6.4 Composition of Functions 

6.5 Substitution and Synthetic Division 

7 Radicals and Exponents 





7.5 Solving Rational Expressions 

7.6 Solving Rational Inequalities 

8 Quadratic Functions 

8.1 Solving Systems of Linear Equations by Graphing 

8.2 Systems of Equations in Two Variables with Applications 



8.5 Matrices (Optional) 


9.1 Solving Equations in One Variable Graphically 

9.2 Solving Linear Inequalities in One Variable Graphically 

9.3 Solving Absolute Value Equations Graphically 

9.4 Solving Absolute Value Inequalities Graphically 




10.3 Operations on Radical Expressions 







11.3 An Introduction to the Parabola 

11.4 Solving Quadratic Inequalities 

12 Conic Sections 

12.1 Conic Sections and the Circle 

12.2 Ellipses 

12.3 Hyperbolas 


13.1 Inverse Relations and Functions 




13.5 Logarithmic and Exponential Equations 

Appendix A 

Appendix A.1 Determinants and Cramer’s Rule 

NEW *9780077350048* 

BEGINNING AND 


The Language and Symbolism 

of Mathematics, 3rd Edition 

By James Hall and Brian Mercer of Parkland 

College 

2011 (January 2010) / 1024 pages 

ISBN: 9780077350048 

www.mhhe.com/hallmercer 

Intended for schools that want a single text covering the standard 

topics from Beginning and Intermediate Algebra. Topics are organized 

by using the principles of the AMATYC standards as a guide, giving 

strong support to teachers using the text. The book’s organization and 

pedagogy are designed to work for students with a variety of learning 

styles and for teachers with varied experiences and backgrounds. 

The inclusion of multiple perspectives -- verbal, numerical, algebraic, 

and graphical -- has proven popular with a broad cross section of 

students. Use of a graphing calculator is assumed. BEGINNING AND 

INTERMEDIATE ALGEBRA: THE LANGUAGE AND SYMBOLISM 

OF MATHEMATICS is a reform-oriented book. 

FEATURES 

Concepts presented using “Rule of Four” (multiple representations 

of mathematical solutions to problems, including graphical, 

algebraic, numerical, and verbal approaches. 

Technology Is Built-In, Not Added-On. The use of technology 

has been woven throughout the text -- it is not simply inserted into a 

standard presentation. 

More Emphasis on Functions -- Chapters 7-11 will have more 

of a functions emphasis than in the first edition of Beginning & Intermediate 

Algebra. 

“Multiple Perspectives” boxes -- One of the most prominent 

features of the text is the use of “Multiple Perspectives” text boxes, 

featuring two or more of the Rule of Four approaches (numerical, 

algebraic, graphical, verbal) to solving a given problem. 

 

The AMATYC Standards guided the development of the book. 

More Emphasis on Functions -- Chapters 7-11 will have more 

of a functions emphasis than in the first edition of Beginning & Intermediate 

Algebra. 

More Exercises! New exercises have been added throughout 

the text. Data has also been updated/revised to reflect more current 

information in some problems. 

Revised Page Layout -- Some of the key pedigogical features 

have been rearranged throughout the chapters. The Self-Check answers 

now appear at the end of each section (not on the same page 

as the questions), and several of the side notes have been moved 

to the main text. 

CONTENTS 

1 Operations with Real Numbers and a Review of Geome 

1.1 Preparing for an Algebra Class 

1.2 The Real Number Line 



1.5 Multiplication of Real Numbers and Natural Number Exponents 

1.6 Division of Real Numbers 


2 Linear Equations and Patterns 

2.1 The Rectangular Coordinate System and Arithmetic Sequences 

24


2.2 Function Notation and Linear Functions 

2.3 Graphs of Linear Equations in Two Variables 

2.4 Solving Linear Equations in One Variable by Using the Addition- 

Subtraction Principle 

2.5 Solving Linear Equations in One Variable by Using the Multiplication-Division 

Principle 

2.6 Using and Rearranging Formulas 

2.7 Proportions and Direct Variation 

2.8 More Applications of Linear Equations 

3 Lines and Systems of Linear Equations in Two Variables 

3.1 Slope of a Line and Applications of Slope 

3.2 Special Forms of Linear Equations in Two Variables 

3.3 Solving Systems of Linear Equations in Two Variables Graphically 

and Numerically 

3.4 Solving Systems of Linear Equations in Two Variables by the 

Substitution Method 

3.5 Solving Systems of Linear Equations in Two Variables by the 

Addition Method 

3.6 More Applications of Linear Systems 

Cumulative Review of Chapters 1-3 

4 Linear Inequalities and Systems of Linear Inequalities 

4.1 Solving Linear Inequalities by Using the Addition-Subtraction 

Principle 

4.2 Solving Linear Inequalities by Using the Multiplication-Divison 

Principle 

4.3 Solving Compound Inequalities 

4.4 Solving Absolute Value Equations and Inequalities 

4.5 Graphing Systems of Linear Inequalities in Two Variables 

5 Exponents and Operations with Polynomials 

5.1 Product and Power Rules for Exponents 

5.2 Quotient Rule and Zero Exponents 


5.4 Adding and Subtracting Polynomials 


5.6 Special Products of Binomials 

5.7 Dividing Polynomials 

Diagonostic Review of Beginning Algebra 


6.1 An Introduction to Factoring Polynomials 

6.2 Factoring Trinomials of the Form x2 + bxy + cy2 

6.3 Factoring Trinomials of the Form ax2 + bxy + cy2 

6.4 Factoring Special Forms 

6.5 Factoring by Grouping and a General Strategy for Factoring 

Polynomials 

6.6 Solving Equations by Factoring 

7 Solving Quadratic Equations 

8 Functions: Linear, Absolute Value, and Quadratic 

8.1 Functions and Representations of Functions 

8.2 Linear and Absolute Value Functions 

8.3 Linear and Quadratic Functions and Curve Fitting 

8.4 Using the Quadratic Formula to find Real Solutions 

8.5 The Vertex of a Parabola and Max-Min Applications 

8.6 More Applications of Quadratic Equations 

8.7 Complex Numbers and Solving Quadratic Equations with Complex 

Solutions 

9 Rational Functions 

9.1 Graphs of Rational Functions and Reducing Rational Expressions 



9.4 Combining Operations and Simplifying Complex Rational Expressions 

9.5 Solving Equations Containing Rational Expressions 

9.6 Inverse and Joint Variation and Other Applications Yielding Equations 

with Fractions 


10 Square Root and Cube Root Functions and Rational Exponents 

10.1 Evaluating Radical Expressions and Graphs of Square Root 

and Cube Root Functions 

10.2 Adding and Subtracting Radical Expressions 

10.3 Multiplying and Dividing Radical Expressions 

10.4 Solving Equations Containing Radical Expressions 

10.5 Rational Exponents and Radicals 


11.1 Geometric Sequences Graphs of Exponential Functions 



11.4 Evaluating Logarithms 



11.7 Exponential Curve Fitting and Other Applications of Exponential 

and Logarithmic Equations 


12 A Preview of College Algebra 

12.1 Solving Systems of Linear Equations by Using Augmented 

Matrices 


12.3 Horizontal and Vertical Translations of the Graphs of Functions 

12.4 Stretching, Shrinking and Reflecting Graphs of Functions 


12.6 Sequences, Series and Summation Notation 

12.7 Conic Sections 

NEW *9780077350086* 

BEGINNING AND 


3rd Edition 

by Julie Miller, Daytona State College-Daytona 

Beach, Molly O’Neill, Daytona State College- 

Daytona Beach, and Nancy Hyde 

2011 (January 2010) / 1184 pages 

ISBN: 9780077350086 


Miller/O’Neill/Hyde continues to offer an enlightened approach 

grounded in the fundamentals of classroom experience in Beginning 

and Intermediate 2e. The practice of many instructors in the classroom 

is to present examples and have their students solve similar problems. 

This is realized through the Skill Practice Exercises that directly follow 

the examples in the textbook. Throughout the text, the authors have 

integrated many Study Tips and Avoiding Mistakes hints, which are 

 

the classroom. In this way, the text communicates to students, the 

very points their instructors are likely to make during lecture, helping 

to reinforce the concepts and provide instruction that leads students 

to mastery and success. The authors included in this edition, Problem- 

Recognition Exercises, that many instructors will likely identify to be 

similar to worksheets they have personally developed for distribution 

to students. The intent of the Problem-Recognition exercises, is to 

help students overcome what is sometimes a natural inclination 

toward applying problem-sovling algorithms that may not always 

be appropriate. In addition, the exercise sets have been revised to 

 

tion. This permits instructors to choose from a wealth of problems, 

allowing ample opportunity for students to practice what they learn 

in lecture to hone their skills and develop the knowledge they need 

to make a successful transition into College Algebra. In this way, the 

book perfectly complements any learning platform, whether traditional 

 

comes from lecture, that students will feel as comfortable outside 

of class, as they do inside class with their instructor. For even more 

support, students have access to a wealth of supplements, including 

McGraw-Hill’s online homework management system, MathZone. 

FEATURES 

Problem Recognition Exercises Developmental math students 

are sometimes conditioned into algorithmic thinking to the point 

25


where they want to automatically apply various algorithms to solve 

problems, whether it is meaningful or not. These exercises were built 

to decondition students from falling into that trap. Carefully crafted by 

the authors, the exercises focus on the situations where students most 

often get “mixed-up.” Working the Problem Recognition Exercises, 

students become conditioned to Stop, Think, and Recall what method 

is most appropriate to solve each problem in the set. 

chapter 7: In Sections 7.1-7.4, we learned how to simplify, add, 

subtract, multiply, and divide rational expressions. The procedure 

for each operation is different, and it takes considerable practice 

to determine the correct method to apply for a given problem. The 

following review exercises give you the opportunity to practice the 

specific techniques for simplifying rational expressions.” 












introduced. 




















CONTENTS 

Chapter R: Reference 

R.1 Study Tips 

R.2 Fractions 

R.3 Introduction to Geometry 

Chapter 1: The Set of Real Numbers 





Problem Recognition Exercises – Addition and Subtraction of Signed 

Numbers 



Chapter 1 Summary 

Chapter 1 Review Exercises 

Chapter 1 Test 



Equality 


2.3 Linear Equations: Clearing Fractions and Decimals 








Cumulative Review Exercises Chapters 1 – 2 

Chapter 3: Graphing Linear Equations in Two Variables 




3.4 Slope-Intercept Form of a Line 







Chapter 4: Systems of Linear Equations in Two Variables 



4.3 Solving Systems of Equations by the Addition Method 

4.4 Applications of Linear Equations in Two Variables 





Chapter 5: Polynomials and Properties of Exponents 



5.3 Definitions of b0 and b-n 

5.4 Scientific Notation Problem Recognition Exercises – Properties 

of Exponents 




Problem Recognition Exercises – Operations on Polynomial 




Cumulative Review Exercises, Chapters 1-5 

Chapter 6: Factoring Polynomials 


6.2 Factoring Trinomials of the form x2 + bx + c (Optional) 




6.6 General Factoring Summary 

6.7 Solving Equations by Using the Zero Product Rule 










Problem Recognition Exercises - Operations on Rational Expressions 


7.6 Rational Equations Problem Recognition Exercises – Comparing 

Rational Equations and Rational Expressions 

7.7 Applications of Rational Equations, Ratios and Proportions 

7.8 Variation (Optional) 





Chapter 8: Introduction to Relations and Functions 

8.1 Introduction to Relations 

26



8.3 Graphs of Functions 

8.4 Variation 




Cumulative Review Exercises, Chapters 1 – 8 

Chapter 9: Systems of Linear Equations in Three Variables 


9.2 Applications of Systems of Linear Equations in Three Variables 

9.3 Solving systems of Linear Equations Using Matrices 

9.4 Determinants and Cramer’s Rule 





Chapter 10: More Equations and Inequalities 

10.1 Compound Inequalities 

10.2 Polynomial and Rational Inequalities 

10.3 Absolute Value Equations 

10.4 Absolute Value Inequalities 

Problem Recognition Exercises – Equations and Inequalities 






Chapter 11: Radicals and Complex Numbers 

11.1 Definition of an nth-Root 






Problem Recognition Exercises – Operations on Radicals 







Chapter 12: Quadratic Equations and Functions 

12.1 Square Root Property and Completing the Square 



12.4 Graphs of Quadratic Functions 

12.5 Vertex of a Parabola and Applications 





Chapter 13: Exponential and Logarithmic Functions 

13.1 Algebra and Composition of Functions 





13.6 The Irrational Number, e 

Problem Recognition Exercises - Logarithmic and Exponential Forms 






Chapter 14: Conic Sections and Nonlinear Systems 

14.1 Distance Formulas and Circles 

14.2 More on the Parabola 


14.4 Nonlinear Systems of Equations in Two Variables 

14.5 Nonlinear Inequalities and Systems of Inequalities 





Beginning Algebra Review: 

Review A Set of Real Numbers 

Review B Linear Equations in One Variable 

Review C Linear Equations in Two Variables 

Review D Systems of Linear Equations in Two Variables 

Review E Polynomials and Properties of Exponents 

Review F Factoring Polynomials and Solving Quadratic Equations 

Review G Rational Expressions 

Appendix 

A.1 Binomial Expansions 

A.2 Sequences and Series 

A.3 Arithmetic and Geometric Sequences and Series 

Student Answer Appendix 

ELEMENTARY AND INTERMEDIATE 

ALGEBRA 

Alternate Hardcover Edition, Third Edition 

By Donald Hutchinson, Stefan Baratto and Barry Bergman of Clackamas 


2008 (February 2007) / 1312 pages 

ISBN: 9780073309316 


 

ementary and intermediate algebra use two different texts, one for 

each course. As a result, students may be required to purchase two 

texts; this can result in a considerable amount of topic overlap. Over 

the last few years, several publishers have issued “combined” texts 

that take chapters from two texts and merge them into a single book. 

This has allowed students to purchase a single text, but it has done 

little to reduce the overlap. The goal of this author team has been to 

produce a text that was more than a combined text. They wanted to 

unify the topics and themes of beginning and intermediate algebra 

 

will prepare students from different mathematical backgrounds for 

college algebra. We believe we have accomplished our goals. For 

students entering directly from an arithmetic or pre-algebra course, 

this is a text that contains all of the material needed to prepare for 

college algebra. It can be offered in two quarters or in two semesters. 

The new Review Chapter found between chapters 6 and 7 serves as 

 

 

that will accommodate those students placing into the second term 

of a two-term sequence. Here is where the Review Chapter is most 

valuable. It gives the students an opportunity to check that they have 

all of the background required to begin in Chapter 7. If the students 

struggle with any of the material in the Review Chapter, they are 

referred to the appropriate section for further review. 

CONTENTS 

0 Prealgebra Review 

0.1 A Review of Fractions 

0.2 Real Numbers 



0.5 Exponents and Order of Operation 

1 From Arithmetic to Algebra 

1.1 Transition to Algebra 



1.4 Sets 

2 Equations and Inequalities 

2.1 Solving Equations by Adding and Subtracting 

2.2 Solving Equations by Multiplying and Dividing 


2.4 Literal Equations and Their Applications 

2.5 Solving Linear Inequalities Using Addition 

27


2.6 Solving Linear Inequalities Using Multiplication 

2.7 Solving Absolute Value Equations (Optional) 

2.8 Solving Absolute Value Inequalities (Optional) 

3 Graphs and Linear Equations 


3.2 The Cartesian Coordinate System 

3.3 The Graph of a Linear Equation 





4.1 Positive Integer Exponents 

4.2 Zero and Negative Exponents and Scientific Notation 



4.5 Multiplication of Polynomials and Special Products 




5.2 Factoring Special Polynomials 

5.3* Factoring Trinomials: Trial and Error 

5.4 Factoring Trinomials: The ac method 



5.7 Problem Solving with Factoring 

6 A Beginning Look at Functions 


6.2 Tables and Graphs 



6.5 Substitution and Synthetic Division 

R A Review of Elementary Algebra 

R.1 From Arithmetic to Algebra 

R.2 Equations and Inequalities 

R.3 Graphs and Linear Equations 

R.4 Exponents and Polynomials 

R.5 A Beginning Look at Functions 

R.6 Factoring Polynomials 






7.5 Solving Rational Expressions 

7.6 Solving Rational Inequalities 

8 Systems of Linear Equations and Inequalities 


8.2 Systems of Equations in Two Variables with Applications 



8.5 Matrices (Optional) 

9 Graphical Solutions 

9.1 Solving Equations in One Variable Graphically 

9.2 Solving Linear Inequalities in One Variable Graphically 

9.3 Solving Absolute Value Equations Graphically 

9.4 Solving Absolute Value Inequalities Graphically 

10 Radicals and Exponents 










11.3 An Introduction to the Parabola 

11.4 Solving Quadratic Inequalities 


12.1 Conic Sections and the Circle 

12.2 Ellipses 

12.3 Hyperbolas 







Appendix A 

Appendix A.1 Determinants and Cramer’s Rule 




2004 / 308 pages 

ISBN: 9780071443166 


CONTENTS 

Preface 







QUIZ 1 





QUIZ 2 






QUIZ 3 







QUIZ 4 






QUIZ 5 




QUIZ 6 

FINAL EXAM 



INDEX 

28


TEACH YOURSELF ALGEBRA 

2nd Edition 

By P Abbott and Hugh Neill 

2003 / 336 pages 

ISBN: 9780071421263 


Teach Yourself Algebra is a great introduction for learners having no 

prior experience with this ancient branch of mathematics. It acquaints 

readers with algebra and its basic components, such as equations, 

exponents, and indices. Then, using many examples and exercises, 

it shows them how to solve equations of all kinds, including linear, 

simultaneous, and quadratic; determine simple sequences and progression; 

and plot graphical representations of quantities. 

Intermediate Algebra 

NEW 

*9780073384573* 


7th Edition 


2012 (January 2011) / 864 pages 

ISBN: 9780073384573 

www.mhhe.com/dugopolski 

Intermediate Algebra, 3e is part of the latest offerings in the successful 

Dugopolski series in mathematics. The author’s goal is to explain 

mathematical concepts to students in a language they can understand. 

 

of terms and concepts written in understandable language. The 

author uses concrete analogies to relate math to everyday experiences. 

For example, when the author introduces the Commutative 

Property of Addition, he uses a concrete analogy that “the price of a 

hamburger plus a Coke is the same as a Coke plus a hamburger”. 






 










management system, MathZone, as well as ALEKS. 

FEATURES 


























work through. 














various ways. Calculator Close-Ups This feature gives your students 

an idea of how and when to use a graphing calculator. Some Calculator 

Close-Ups simply introduce the features of a graphing calculator, 

where others enhance understanding of algebraic concepts. For this 

reason, many of the Calculator Close-Ups will benefit even those 

students who do not use a graphing calculator. Study Tips - Two 

study tips now precede every exercise set. They give the student 

information on best practices for studying, learning, and performing 

well academically. Helpful Hints are succinct explanations adjacently 

located to a topic. They enhance the chapter material by providing 

another way of approaching a problem, or clearing up misconceptions. 




Warm-up Exercises are ten simple true or false questions located 

at the end of every section. These exercises are designed to 

provide a smooth transition between the concepts in the section and 

the exercise sets. Helping your students recognize that many ideas 

in mathematics are either true or false can assist them in developing 

a broader understanding of the concepts. The exercises can be 

beneficial for in class discussions or group work. 









29















The Wrap-up includes the following: 

Summary is a list of important concepts along with brief illustrative 

examples of each. 

Enriching Your Mathematical Word Power enables students to 

test their recall of new terminology in a multiple-choice format. 

Review Exercises contain problems that are linked to the exact 

chapter and section the concept originally appears as well as a 

miscellaneous section with a mixed set of problems with no chapter 

or section links. 

The Chapter Test is designed to help your student ensure his or 

her preparedness and success for an upcoming exam. The Chapter 

Test does not have linked exercises, thus enabling the student to 

work independently of the sections and examples. All answers to the 

Chapter Test are provided at the back of the book and all worked out 

solutions are provided in the Student Solutions Manual. 













CONTENTS 

PREFACE 


1 The Real Numbers 

1.1 Sets 


1.3 Operations on the Set of Real Numbers 

1.4 Evaluating Expressions and the Order of Operations 


1.6 Using the Properties 











3.3 Three Forms for the Equation of a Line 

3.4 Linear Inequalities and Their Graphs 



4.1 Solving Systems by Graphing and Substitution 



4.4 Solving Linear Systems Using Matrices 




5.1 Integral Exponents and Scientific Notation 

5.2 The Power Rules 

5.3 Polynomials and Polynomial Functions 

5.4 Multiplying Binomials 

5.5 Factoring Polynomials 

5.6 Factoring ax² + bx + c 

5.7 Factoring Strategy 


6 Rational Expressions and Functions 

6.1 Properties of Rational Expressions and Functions 





6.6 Solving Equations Involving Rational Expressions 



7.1 Radicals 






8 Quadratic Equations, Functions, and Inequalities 






9 Additional Function Topics 





9.5 Variation 












12 Sequences and Series (Available online at www.mhhe.com/ 

dugopolski) 


12.2 Series 




Appendix A 


Index 

30


NEW *9780073406176* 


By Sherri Messersmith, College of Dupage 


ISBN: 9780073406176 

www.mhhe.com/messersmith 

Intermediate Algebra, 1e, authored by Sherri Messersmith presents 

content in bite-size pieces, focusing not only on learning mathematical 

concepts, but also explaining the why behind those concepts. For 

students, learning mathematics is not just about the memorization of 

concepts and formulas, but it is also about the journey of learning 

how to problem solve. By breaking the sections down into manage- 

 

traditionally struggle, and then assists them in understanding that material 

to be successful moving forward. Proven pedagogical features, 

such as You Try problems after each example, reinforce a student’s 

mastery of a concept. While teaching in the classroom, Messersmith 

has created worksheets for each section that fall into three categories: 

review worksheets/basic skills, worksheets to teach new content, 

and worksheets to reinforce/pull together different concepts. These 

worksheets are a great way to both enhance instruction and to give 

the students more tools to be successful in studying a given topic. The 

 

 

it important to not only provide quality, but also an abundant quantity 

of exercises and applications. The book is accompanied by numerous 








FEATURES 

Putting It All Together: Several chapters contain a Putting It All 

Together section. In keeping with the author’s philosophy of breaking 

sections into manageable chunks, Messersmith includes this feature 

where needed to help the student to synthesize key topics before 

moving onto the rest of the chapter. 

Worksheets: There are worksheets for each section that fall into 

several categories: guided lecture notes, review worksheets/basic 

skills, worksheets to teach new content, and worksheets to reinforce/ 

pull together different concepts. These worksheets are a great way 

to both enhance instruction and to give the students more tools to be 

successful in studying a given topic. These will be available online 

through Connect Hosted by ALEKS. 

In-Class Examples: In order to give the instructors additional 

material to use in the classroom, a matching In-Class Example is 

provided in the margin of the AIE for every example in the book. 

You Try Problems: After nearly every example, there is a “You 

Try” problem that mirrors that example. This provides students with 

the opportunity to practice a problem similar to what the instructor 

has presented before moving on to the next concept. Answers are 

provided at the end of the section for immediate feedback. 










Be Careful Boxes: There are some mistakes that are very common 

for students to make. The “Be Careful!” boxes make students 

aware of these common errors so that, hopefully, they will not make 

these mistakes themselves. 

Using Technology Boxes: For those instructors who want to 

make use of graphing calculator-related material, Using Technology 

Boxes are included at the ends of sections where relevant. For those 

instructors who don’t want to use this material, they are easily skipped. 

End-of-Section Exercise: The end-of-section exercise sets have 

been organized similarly to the examples—they are presented from 

the most basic to the most rigorous so that students may see how 

the concepts work at the simplest level before progressing to more 

difficult problems. Mixed exercise subsets are also provided where 

students must figure out how to solve problems that look similar but 

cover different objectives. Messersmith has incorporated interesting 

real-world, up-to-date, relevant information that will appeal to students 

of all backgrounds into the applications in the book. Students have 

identified a number of the problems as interesting and fun in previous 

use. Within these exercises, students and faculty will find video, 

calculator, and writing exercise icons. 

Chapter Summary: The comprehensive Summaries at the end 

of each chapter enable students to review important concepts. A 

definition or concept is presented, along with a related example and 

a page reference from the relevant section. 

End-of-Chapter Material: At the end of each chapter, you will 

find a set of Review Exercises, a Chapter Test, and a comprehensive 

Cumulative Review (starting with Chapter 2.) 

New Fill It In exercises take a student through the process of 

working out a problem step-by-step so that students have to provide 

the reason for each mathematical step to solve the problem, much 

like a geometry proof. 

New Guided Student Notes are an amazing resource for instructors 

to help their students become better note-takers. They contain 

in-class examples provided in the margin of the text along with additional 

examples not found in the book to emphasize the give topic 

so that students have less time copying down information and more 

time engaging within the classroom. 

CONTENTS 

1 Real Numbers and Basic Geometry Concepts1.1 Sets of 

Numbers 

1.2 Operations on Real Numbers 



2.1 Solving Linear Equations in One Variable 



2.4 More Applications of Linear Equations 

2.5 Linear Inequalities in One Variable 

2.6 Compound Inequalities in One Variable 


3 Linear Equations in Two Variables and Functions 


3.2 Slope of a Line and Slope-Intercept Form 


3.4 Linear and Compound Linear Inequalities in Two Variables 


31


4 Solving Systems of Linear Equations 

4.1 Solving Systems of Linear Equations in Two Variables 

4.2 Solving Systems of Linear Equations in Three Variables 

4.3 Applications of Systems of Linear Equations 

4.4 Solving Systems of Linear Equations Using Matrices 

5 Polynomials and Polynomial Functions 


5.2 More on Exponents and Scientific Notation 

5.3 Addition and Subtraction of Polynomials and Polynomial Functions 

5.4 Multiplication of Polynomials and Polynomial Functions 

5.5 Division of Polynomials and Polynomial Functions 



6.2 Factoring Trinomials 

6.3 Special Factoring Techniques 




7 Rational Expressions, Equations, and Functions 

7.1 Simplifying, Multiplying, and Dividing Rational Expressions and 

Functions 





7.5 Applications of Rational Equations 

7.6 Variation 


8.1 Radical Expressions and Functions 


8.3 Simplifying Expressions Containing Square Roots 

8.4 Simplifying Expressions Containing Higher Roots 






9 Quadratic Equations and Functions 





9.4 Formulas and Applications 


9.6 Applications of Quadratic Functions and Graphing Other Parabolas 

9.7 Quadratic and Rational Inequalities 

10 Exponential, and Logarithmic Functions 

10.1 Composite and Inverse Functions 




10.5 Common and Natural Logarithms and Change of Base 


11 Nonlinear Functions, Conic Sections, and Nonlinear Systems 

11.1 Graphs of Other Useful Functions 

11.2 The Distance Formula, Midpoint, and Circle 

11.2 The Ellipse 

11.3 The Hyperbola 



11.5 Second-Degree Inequalities and Systems of Inequalities 

12 Sequences and Series (Online Only) 

12.1 Sequences and Series 




A Appendix 

A.1 Geometry Review 

A.2 Determinants and Cramer’s Rule 

A.3 Graphing Polynomial Functions 

A.4 Synthetic Division and the Remainder Theorem 

NEW *9780077349943* 


3rd Edition 

by Julie Miller, Daytona State College-Daytona 

Beach, Molly O’Neill, Daytona State College- 

Daytona Beach, and Nancy Hyde 

2011 (January 2010) \ Hardcover / 960 pages 

ISBN: 9780077349943 


Intermediate Algebra continues to offer an enlightened approach 

grounded in the fundamentals of classroom experience. Throughout 

the text, the authors have integrated many Study Tips and Avoiding 

 

presented to students in the classroom. 

FEATURES 












introduced. 



















32



CONTENTS 

Chapter 1: Review of Basic Algebraic Concepts 

1.1 Sets of Numbers and Interval Notation 

1.2 Operations on Real Numbers 




1.6 Literal Equations and Applications to Geometry 


1.8 Properties of Integer Exponents and Scientific Notation 




Chapter 2: Linear Equations in Two Variables 

2.1 The Rectangular Coordinate System and Midpoint Formula 



2.4 Equations of a Line 

2.5 Applications of Linear Equations and Graphing 





Chapter 3: Systems of Linear Equations 


3.2 Solving Systems of Equations by Using the Substitution Method 

3.3 Solving Systems of Equations by Using the Addition Method 

3.4 Applications of Systems of Linear Equations in Two Variables 

3.5 Systems of Linear Equations in Three Variables and Applications 

3.6 Solving Systems of Linear Equations by Using Matrices 






Chapter 4: Introduction to Relations and Functions 



4.3 Graphs of Functions 

4.4 Variation 





Chapter 5:Polynomials 

5.1 Addition and Subtraction of Polynomials and Polynomial Functions 



Problem Recognition Exercises – Operations on Polynomials 




5.7 Additional Factoring Strategies 






Chapter 6:Rational Expressions and Rational Equations 

6.1 Rational Expressions and Rational Functions 




Problem Recognition Exercises – Operations on Rational Expressions 

6.5 Rational Equations 






Chapter 7: Radicals and Complex Numbers 

7.1 Definition of an nth Root 











Chapter 8: Quadratic Equations and Functions 





8.5 Vertex of a Parabola and Applications 




Cumulative Review Exercises, Chapters 1 - 8 

Chapter 9: More Equations and Inequalities 




9.4 Absolute Value Inequalities 

Problem Recognition – Equations and Inequalities 












10.6 The Irrational Number e 

Problem Recognition – Logarithmic and Exponential Forms 






Chapter 11: Conic Sections 

11.1 Distance Formula and Circles 

11.2 More on the Parabola 



11.5 Nonlinear Inequalities and Systems of Inequalities 





Appendix 




33



2nd Edition 




ISBN: 9780077281113 

ISBN: 9780077304256 [Alternate Edition hardcover] 


Intermediate Algebra offers a refreshing approach to the traditional 

content of the course. Presented in worktext format, Intermediate Algebra 

offers a review of problem solving, solving equations in two and 

three variables, a chapter devoted to functions, polynomials, radicals 

and complex numbers, factoring and quadratic functions, rational 

expressions, and inequalities. Other topics include exponential and 

 

sion and insight of its experienced author team with features devel- 

 

CONTENTS 

Chapter 1 Review of Basic Algebraic Concepts 

1.1 Sets of Number and Interval Notation 

1.2 Operation on Real Numbers 


1.4 Linear Equations in One Variable--Problem Recognition Exercises: 

Expressions and Equations 


1.6 Literal Equations and Applications to Geometry 


1.8 Properties of Integer Exponents and Scientific Notation 

Chapter 2 Graphing Linear Equations and Functions 


2.2 Slope of a Line--Problem Recognition Exercises: Intercepts and 

Slope 

2.3 Equations of a Line 

2.4 Application of Linear Equations and Modeling 



2.7 Graphs of Basic Functions 

Chapter 3 Systems of Linear Equations 


3.2 Solving Systems of Linear Equations by Using the Substitution 

Method 

3.3 Solving Systems of Linear Equations by Using the Addition 

Method-- Problem Recognition Exercises: Method of Solving Systems 

of Equations 

3.4 Applications of Systems of Linear Equations in Two Variables 

3.5 Systems of Linear Equations in Three Variables and Applications 

3.6 Solving Systems of Linear Equations by Using Matrices 

Chapter 4 Polynomials 

4.1 Addition and Subtraction of Polynomials and Polynomial Functions. 


4.3 Division of Polynomials--Problem Recognition Exercises: Operations 

on Polynomials 




4.7 Additional Factoring Strategies 


Chapter 5 Rational Expressions and Rational Equations 

5.1 Rational Expressions and Rational Functions 



5.4 Complex Fractions--Problem Recognition Exercises: Simplifying 

Rational Expressions 

5.5 Solving Rational Equations--Problem Recognition Exercises: 

Rational Expressions and Equations 


5.7 Variation 

Chapter 6 Radicals and Complex Numbers 

6.1 Definition of an nth-Root 




6.5 Multiplication of Radicals--Problem Recognition Exercises: Operations 

on Radical Expressions 




Chapter 7 Quadratic Equations and Functions 



7.3 Equations in Quadratic Form--Problem Recognition Exercises: 

Recognizing Equation Types 


7.5 Applications of Quadratic Functions and Modeling 

Chapter 8 More Equations and Inequalities 




8.4 Absolute Value Inequalities--Problem Recognition Exercises: 

Equations and Inequalities 


Chapter 9 Exponential and Logarithmic Functions 






9.6 The Irrational Number e--Problem Recognition Exercises: Logarithmic 

and Exponential Forms 

9.7 Exponential and Logarithmic Equations 

Chapter 10 Conic Sections 

10.1 Distance Formula, Midpoint, and Circles 

10.2 More of the Parabola 

10.3 The Ellipse and Hyperbola--Problem Recognition Exercises: 

Identifying and Graphing Conic Sections 


10.5 Nonlinear Inequalities and System if Inequalities 

Additional Topics Appendix 


A.2 Determinants and Cramer’s Rule 




3rd Edition 

by Ignacio Bello, University Of South Florida-Tampa, and Fran Hopf, 

University Of South Florida-Tampa 

2009 / Paper / 960 pages 

ISBN: 9780077224806 

www.mhhe.com/bello 

Intermediate Algebra prepares students for further courses in the college 

math curriculum. Students of all backgrounds will be delighted to 

 

out to diverse demographics. Through down-to-earth explanations, 

patient skill-building, and exceptionally interesting and realistic applications, 

this worktext will empower students to learn and master 

algebra in the real world. 

CONTENTS 

Chapter 1: The Real Numbers 

1.1 Numbers and Their Properties 

1.2 Operations and Properties of Real Numbers 

1.3 Properties of Exponents 

1.4 Algebraic Expressions and the Order of Operations 


34



2.2 Formulas, Geometry, and Problem Solving 

2.3 Problem Solving: Integers and Geometry 

2.4 Problem Solving: Percent, Investment, Motion, and Mixture 

Problems 

2.5 Linear and Compound Inequalities 

2.6 Absolute-Value Equations and Inequalities 

Chapter 3: Graphs and Functions 

3.1 Graphs 

3.2 Using Slopes to Graph Lines 

3.3 Equations of Lines 



3.6 Linear Functions 

Chapter 4: Solving Systems of Linear Equations and Inequalities 

4.1 Systems with Two Variables 

4.2 Systems with Three Variables 

4.3 Coin, Distance-Rate-Time, Investment, and Geometry Problems 


Chapter 5: Polynomials 

5.1 Polynomials: Addition and Subtraction 




5.5 Special Factoring 

5.6 General Methods of Factoring 

5.7 Solving Equations by Factoring: Applications 


6.1 Rational Expressions 




6.5 Division of Polynomials and Synthetic Division 

6.6 Equations Involving Rational Expressions 

6.7 Applications: Problem Solving 

6.8 Variation 

Chapter 7: Rational Exponents and Radicals 

7.1 Rational Exponents and Radicals 


7.3 Operations with Radicals 

7.4 Solving Equations Containing Radicals 


Chapter 8: Quadratic Equations and Inequalities 

8.1 Solving Quadratics by Completing the Square 

8.2 The Quadratic Formula: Applications 

8.3 The Discriminant and Its Applications 

8.4 Solving Equations in Quadratic Form 

8.5 Nonlinear Inequalities 

Chapter 9: Quadratic Functions and the Conic Sections 


9.2 Circles and Ellipses 

9.3 Hyperbolas and Identification of Conics 


9.5 Nonlinear Systems of Inequalities 

Chapter 10: Functions-Inverse, Exponential, and Logarithmic 

10.1 The Algebra of Functions 



10.4 Logarithmic Functions and Their Properties 

10.5 Common and Natural Logarithms 

10.6 Exponential and Logarithmic Equations and Applications 

Appendix A: Sequences and Series 

A1: Matrices 

A2: Determinants and Cramer’s Rule 

A3: Sequences and Series 

A4: Arithmetic Sequences and Series 

A5: Geometric Sequences and Series 

A6: The Binomial Expansion 


By Donald Hutchison, Stefan Baratto, Clackamas Community College, 

Kelly Kohlmetz, University of Wisconsin-Milwaukee and Barry Bergman 

2008 / 1120 pages 

ISBN: 9780073309309 

www.mathzone.com/hutchison 

Intermediate Algebra by Baratto/Kohlmetz/Bergman is part of the 

latest offerings in the successful Streeter-Hutchison Series in Mathematics. 

By popular demand, we are now offering an Intermediate 

Algebra book in the series again. This book combines the best of 

earlier versions of Intermediate Algebra, along with new material 

requested by a cross-section of Intermediate Algebra instructors 

 

of encouraging the learning of mathematics by focusing its coverage 

on mastering math through practice. This worktext seeks to provide 

carefully detailed explanations and accessible pedagogy to introduce 

intermediate algebra concepts and put the content in context. The 

authors use a three-pronged approach (I. Communication, II. Pattern 

Recognition, and III. Problem Solving) to present the material and 

stimulate critical thinking skills. Items such as Math Anxiety boxes, 

Check Yourself exercises, and Activities represent this approach and 

the underlying philosophy of mastering math through practice. The 

exercise sets are well-organized, and clearly labeled. Vocational and 

professional-technical exercises have been included throughout. 

Repeated exposure to this consistent structure should help advance 

the student’s skills in relating to mathematics. The book is designed 

for a one-semester intermediate algebra course and is appropriate 

for lecture, learning center, laboratory, or self-paced courses. It is accompanied 

by numerous useful supplements, including McGraw-Hill’s 

online homework management system, MathZone. 

CONTENTS 


1.1 The Set of Real Numbers 

1.2 Operations and Properties 

1.3 Inequalities and Absolute Values 


1.5 Properties of Exponents and Scientific Notation 


2.1 Solutions of Linear Equations in One Variable 

2.2 Literal Equations and Formulas 

2.3 Applications and Problem Solving 



3 Graphs of Linear Relations and Functions 

3.1 Graphing Linear Equations 

3.2 An Introduction to Functions 



3.5 Graphing Absolute Value Functions and Linear Inequalities 

4 Systems of Linear Relations 

4.1 Systems of Linear Equations in Two Variables 


4.3 Solving Systems of Equations Using Matrices 

4.4 Graphing Systems of Linear Inequalities 

5 Polynomials and Polynomial Functions 




5.4 Common Factors and Factoring by Grouping 

5.5 Factoring Special Binomials 

5.6 Factoring Trinomials: Trial and Error 

5.7 Factoring Trinomials: The ac Method 




6.1 Simplification of Rational Expressions and Functions 





6.6 Variation 

35


7 Radical and Radical Exponents 


7.2 Simplification of Radical Expressions 



7.5 Geometric and Other Applications 




8.1 Graphing Factorable Quadratic Functions 


8.3 Solving Quadratic Equations by Using the Quadratic Formula 

8.4 Solving Equations that are Quadratic in Form 

8.5 Quadratic Inequalities and Rational Inequalities 


9.1 Parabolas 

9.2 Circles 

9.3 Ellipses and Hyperbolas 

9.4 Nonlinear Systems 

10 Additional Properties of Functions 








11.4 Solving Logarithmic and Exponential Equations 

Appendix: Determinants and Cramer’s Rule 


SCHAUM’S OUTLINE OF INTERMEDIATE 

ALGEBRA 

2nd Edition 

By Ray Steege and Kerry Bailey, Laramie County Community College, 

Wyoming 

2010 (April 2010) / Softcover / 416 pages 

ISBN: 9780071629980 


Schaum’s Outline of Intermediate Algebra, Second Edition covers 

the concepts typically found in the intermediate algebra course, 

including: fundamental concepts, polynomials, rational expressions, 

 

radicals, systems of equations and inequalities, relations and function, 

exponential and logarithmic functions, sequences, series, and 

the binomial theorem. 



2004 / 308 pages 

ISBN: 9780071443166 


CONTENTS 

Preface 







QUIZ 1 





QUIZ 2 






QUIZ 3 







QUIZ 4 






QUIZ 5 




QUIZ 6 

FINAL EXAM 



INDEX 




 




36


SCHAUM’S EASY OUTLINE INTERMEDIATE 

ALGEBRA 

By Ray Steege and Kerry Bailey, Laramie County Community 

College, Wyoming 

2004 / Softcover / 144 pages 

ISBN: 9780071422437 


What could be better than the bestselling Schaum’s Outline series? 

For students looking for a quick nuts-and-bolts overview, it would have 

to be Schaum’s Easy Outline series. Every book in this series is a 

 

sor. With an emphasis on clarity and brevity, each new title features 

a streamlined and updated format and the absolute essence of the 

subject, presented in a concise and readily understandable form. 

Graphic elements such as sidebars, reader-alert icons, and boxed 

highlights stress selected points from the text, illuminate keys to learning, 

and give students quick pointers to the essentials. 

Designed to appeal to underprepared students and readers 

turned off by dense text 

Cartoons, sidebars, icons, and other graphic pointers get the 

material across fast 

 

Concise text focuses on the essence of the subject 

Deliver expert help from teachers who are authorities in their 

fields 

 

 

Perfect for last-minute test preparation 

So small and light that they fit in a backpack! 


2nd Edition 


2003 / 336 pages 

ISBN: 9780071421263 









TEST YOURSELF: INTERMEDIATE ALGEBRA 

By Joan Van Glabek 

1996 / 192 pages 

ISBN: 9780844223612 


(Details unavailable at press time) 

Algebra for College Students 

NEW *9780073384344* 

ALGEBRA FOR COLLEGE 

STUDENTS 

6th Edition 


2012 (January 2011) / 928 pages 

ISBN: 9780073384344 

www.mhhe.com/math/devmath/dugopolski/ 

Algebra for College Students, 6e is part of the latest offerings in the 

successful Dugopolski series in mathematics. The author’s goal is 

to explain mathematical concepts to students in a language they can 

 

explanations of terms and concepts written in understandable language. 

The author uses concrete analogies to relate math to everyday 

experiences. For example, when the author introduces the Commutative 

Property of Addition, he uses a concrete analogy that “the price of 

a hamburger plus a Coke is the same as a Coke plus a hamburger”. 






 















FEATURES 

















37











work through. 











various ways. Calculator Close-Ups This feature gives your students 

an idea of how and when to use a graphing calculator. Some Calculator 

Close-Ups simply introduce the features of a graphing calculator, 

where others enhance understanding of algebraic concepts. For this 

reason, many of the Calculator Close-Ups will benefit even those 

students who do not use a graphing calculator. Study Tips - Two 

study tips now precede every exercise set. They give the student 

information on best practices for studying, learning, and performing 

well academically. Helpful Hints are succinct explanations adjacently 

located to a topic. They enhance the chapter material by providing 

another way of approaching a problem, or clearing up misconceptions. 




Warm-up Exercises are ten simple true or false questions located 

at the end of every section. These exercises are designed to 

provide a smooth transition between the concepts in the section and 

the exercise sets. Helping your students recognize that many ideas 

in mathematics are either true or false can assist them in developing 

a broader understanding of the concepts. The exercises can be 

beneficial for in class discussions or group work. 






















The Wrap-up includes the following: Summary is a list of important 

concepts along with brief illustrative examples of each. Enriching 

Your Mathematical Word Power enables students to test their recall 

of new terminology in a multiple-choice format. Review Exercises 

contain problems that are linked to the exact chapter and section the 

concept originally appears as well as a miscellaneous section with a 

mixed set of problems with no chapter or section links. The Chapter 

Test is designed to help your student ensure his or her preparedness 

and success for an upcoming exam. The Chapter Test does not have 

linked exercises, thus enabling the student to work independently 

of the sections and examples. All answers to the Chapter Test are 

provided at the back of the book and all worked out solutions are 

provided in the Student Solutions Manual. 













CONTENTS 

PREFACE 



1.1 Sets 


1.3 Operations on the Set of Real Numbers 

1.4 Evaluating Expressions and the Order of Operations 


1.6 Using the Properties 











3.3 Three Forms for the Equation of a Line 

3.4 Linear Inequalities and Their Graphs 




4.1 Solving Systems by Graphing and Substitution 



4.4 Solving Linear Systems Using Matrices 




5.1 Integral Exponents and Scientific Notation 

5.2 The Power Rules 

5.3 Polynomials and Polynomial Functions 

5.4 Multiplying Binomials 

5.5 Factoring Polynomials 

5.6 Factoring ax² + bx + c 

5.7 Factoring Strategy 



6.1 Properties of Rational Expressions and Functions 





6.6 Solving Equations Involving Rational Expressions 


38



7.1 Radicals 












9 Additional Function Topics 





9.5 Variation 

10 Polynomial and Rational Functions 

10.1 The Factor Theorem 

10.2 Zeros of a Polynomial Function 

10.3 The Theory of Equations 

10.4 Graphs of Polynomial Functions 

10.5 Graphs of Rational Functions 












13 Sequences and Series 


13.2 Series 




14 Counting and Probability 

14.1 Counting and Permutations 

14.2 Combinations 

14.3 Probability 

Appendix A 


Index 

SCHAUM’S OUTLINE OF COLLEGE 

ALGEBRA 

3rd Edition 

By Murray R Spiegel (deceased) and Robert Moyer, Fort Valley State 

School 

2010 (August 2009) / 416 pages 

ISBN: 9780071635394 


A complete but economically written guide to college algebra, for 

students in four-year colleges, two-year colleges, or high school taking 

courses variously titled College Algebra, Precalculus, Algebra I, 

Algebra II, Linear Algebra, Arithmetic and Topics in Algebra, or Functions 

and Graphs. Course material in outline form is accompanied by 

nearly 2000 problems with careful, detailed solutions. 

CONTENTS 

1. Fundamental Operations with Numbers 

2. Fundamental Operations with Algebraic Expressions 

3. Properties of Numbers 

4. Special Products 

5. Factoring 

6. Fractions 

7. Exponents 

8. Radicals 

9. Simple Operations with Complex Numbers 

10. Equations in General 

11. Ratio, Proportion, and Variation 

12. Functions and Graphs 

13. Linear Equations in One Variable 

14. Equations of Lines 

15. Simultaneous Linear Equations 

16. Quadratic Equations in One Variable 

17. Conic Sections 

18. Systems of Equations Involving Quadratics 

19. Inequalities 

20. Polynomial Functions 

21. Rational Functions 

22. Sequences and Series 

23. Logarithms 

24. Permutations and Combinations 

25. The Binomial Theorem 


27. Determinants 

28. Matrices 

29. Mathematical Induction 

30. Partial Fractions 

SCHAUM’S OUTLINE OF MATHEMATICAL 

HANDBOOK OF FORMULAS AND TABLES 

3rd Edition 

by Murray R. Spiegel (deceased), Seymour Lipschutz, Temple University- 

Philadelphia, and John Liu, University of Maryland 


ISBN: 9780071548557 


This third edition covers elementary concepts in algebra, geometry, 

etc. and more advanced concepts in differential equations and vector 

analysis. It also expands its section on Probability and Statistics and 

includes a new section on Financial Mathematics to keep up with the 

 

math and the sciences. 

CONTENTS 

Formulas: 

1. Elementary Constants, Products, Formulas 

2. Geometry 

3. Elementary Transcendental Functions 

4. Calculus 

5. Differential Equations and Vector Analysis 

6. Series 

7. Special Functions and Polynomials 

8. Laplace and Fourier Transforms 

9. Elliptic and Miscellaneous Special Functions 

10. Inequalities and Infinite Products 

11. Probability and Statistics 

12. Numerical Methods 

Tables: 

1. Logarithmic, Trigonometric, Exponential Functions 

2. Factorial and Gamma Function, Binomial Coefficients 

3. Bessel Functions 

4. Legendre Polynomials 

5. Elliptic Integrals 

6. Financial Tables 


39





2004 / 308 pages 

ISBN: 9780071443166 


CONTENTS 

Preface 







QUIZ 1 





QUIZ 2 






QUIZ 3 







QUIZ 4 






QUIZ 5 




QUIZ 6 

FINAL EXAM 



INDEX 


2nd Edition 


2003 / 336 pages 

ISBN: 9780071421263 












 




REVIEW COPY 










40

Business Mathematics........................................................................................53 

Discrete Mathematics .........................................................................................48 

Finite Mathematics .............................................................................................53 

Geometry ............................................................................................................43 


Liberal Arts Mathematics ....................................................................................44 

Mathematics for Elementary Teachers ...............................................................46 

Technical Mathematics .......................................................................................50 



41

New Titles 



Mathematics for Elementary Teachers: A Conceptual Approach, 9e Bennett 9780073519579 46 

Mathematics for Elementary Teachers: An Activity Approach, 9e Bennett 9780077430917 47 

Discrete Mathematics and Its Applications, 7e Rosen 9780073383095 48 



Mathematics in Our World, 2e Sobecki 9780077356651 44 

42


Geometry 

SCHAUM’S EASY OUTLINES: GEOMETRY 

2nd Edition 

By Barnett Rich (deceased) 

2011 (September 2010) / 144 pages 

ISBN: 9780071745857 


When you need just the essentials of geometry, this Easy Outlines 

book is there to help. 

If you are looking for a quick nuts-and-bolts overview of geometry, it’s 

got to be Schaum’s Easy Outline. This book is a pared-down, simpli- 

 

an emphasis on clarity and conciseness. 


highlights stress selected points from the text, illuminate keys to 

learning, and give you quick pointers to the essentials. 

• Perfect if you have missed class or need extra review 

• Gives you expert help from teachers who are authorities in their 

fields 

• So small and light that it fits in your backpack! 

Topics include: Lines, Angles, and Triangles, Deductive Reasoning, 

Triangles, Parallel Lines, Distances, and Angle Sums, Trapezoids 

and Parallelograms, Circles, Similarity, Areas, Regular Polygons 

and the Circle, Constructions, Formulas for Reference, Proofs of 

Important Theorems 

CONTENTS 

1. Lines, Angles, and Triangles; 

2. Deductive Reasoning; 

3. Congruent Triangles; 

4. Parallel Lines, Distances, and Angle Sums; 

5. Trapezoids and Parallelograms; 

6. Circles; 

7. Similarity; 

8. Areas; 

9. Regular Polygons and the Circle; 

10. Constructions; 

Appendix A: Formulas for Reference; 

Appendix B: Proofs of Important Theorems 

SCHAUM’S OUTLINE OF GEOMETRY 

4th Edition 

By Barnett Rich (deceased) and Christopher Thomas 

2009 (July 2008) / 369 pages 

ISBN: 9780071544122 


A classic Schaum’s bestseller, thoroughly updated to match the latest 

course scope and sequence. The ideal review for the hundreds of 

thousands of college and high school students who enroll in geometry 

courses 

CONTENTS 

1. Fundamentals of Algebra: Laws and Operations 

2. Fundamentals of Algebra: Equations and Formulas 

3. Lines, Angles, and Triangles 

4. Methods of Proof 

5. Congruent Triangles 

6. Parallel Lines, Distances, and Angle Sums 

7. Parallelograms, Trapezoids, Medians, and Midpoints 

8. Circles 

9. Similarity 

10. Areas 

11. Regular Polygons and the Circle 

12. Locus 

13. Inequalities and Indirect Reasoning 

14. Improvement of Reasoning 

15. Constructions 

16. Proofs of Important Theorems 

17. Transformational Geometry 


MILLER’S GEOMETRY FOR THE CLUELESS 

2nd Edition 

By Bob Miller, City College of the City University of New York 

2006 / 160 pages 

ISBN: 9780071459020 


CONTENTS 

What is Geometry? Why Should I Take It? 

CHAPTER 1 The Basics: Undefined Words, Defined Words, Axioms, 

and Postulates 

CHAPTER 2 The Beginnings of Proofs 

CHAPTER 3 Improvement of Reasoning: Statement, Converse, 

Inverse, Contrapositive; Necessary and Sufficient Conditions; If and 

Only If 

CHAPTER 4 Parallel Lines, Forever Together 

CHAPTER 5 Mostly Triangles 

CHAPTER 7 Similar Figures and Pythagoras Lives!!! 

CHAPTER 8 Quadrilaterals Squarely Done 

CHAPTER 9 Interior and Exterior Angles 

CHAPTER 10 Areal Search & Securing the Perimeter 

CHAPTER 11 Volumes and Surface Areas 

CHAPTER 12 Circle I 

CHAPTER 13 Lines (The Straight Kind) and Parabolas I (Not Straight) 

CHAPTER 14 Distance Formula, Midpoint Formula, Circle II, and 

Analytic Geometry Proofs 

CHAPTER 15 Functions, Translantions, Stretches, Contractions, 

and Flips 

CHAPTER 16 

CHAPTER 17 Right and Not So Right-Angle Trig, Law of Sines, and 

Law of Cosines 

CHAPTER 18 Constructions 

CHAPTER 19 Indirect Proofs; Disproving by Counterexample; and 

Too Much, Just Enough, or Not Enough 

CHAPTER 20 Miscellaneous: Locus; Parallel Lines; and Larger and 

Smaller Sides and Angles 

CHAPTER 21 Twenty-First-Century SAT Spin on Geometry 

CHAPTER 22 Always-Sometimes-Never Questions 

CHAPTER 23 Answers: You Should Always Draw the Picture If You 

Are Having Problems 

Appendix: A Radical Chapter 

Index 

Acknowlegement 

About Bob Miller... In His Own Words 

43


GEOMETRY DEMYSTIFIED 


2003 / 310 pages 

ISBN: 9780071416504 


CONTENTS 

Preface 

PART ONE: TWO DIMENSIONS 

Chapter 1. Some Basic Rules 

Chapter 2. Triangles 

Chapter 3. Quadrilaterals 

Chapter 4. Other Plane Figures 

Chapter 5. Compass and Straight Edge 

Chapter 6. The Cartesian Plane 


PART TWO: THREE DIMENSIONS AND UP 

Chapter 7. An Expanded Set of Rules 

Chapter 8. Surface Area and Volume 

Chapter 9. Vectors and Cartesian Three-Space 

Chapter 10. Alternative Coordinates 

Chapter 11. Hyperspace and Warped Space 


FINAL EXAM 

ANSWERS TO QUIZ, TEST, AND EXAM QUESTIONS 

SUGGESTED ADDITIONAL REFERENCES 

INDEX 

Liberal Arts Mathematics 

NEW *9780077356651* 

MATHEMATICS IN OUR 

WORLD 

2nd Edition 

By David Sobecki, Miami University, Allan 

Bluman, and Angie Matthews, Broward Community 

College 

2011 (January 2010) / 896 pages 

ISBN: 9780077356651 

www.mhhe.com/sobecki 

The author team of Dave Sobecki, Angela Matthews, and Allan 

Bluman have worked together to create the second edition of Mathematics 

in Our World, an engaging text catered to the needs of 

today’s liberal arts mathematics students. This revision focuses strict 

attention to a clear and friendly writing style, integration of numerous 

relevant real-world examples and applications, and implementation 

of the step-by-step approach used for years in Bluman’s Elementary 

Statistics: A Step by Step Approach. The result is an exceptionally 

engaging text that is able to both effectively and creatively convey 

the basic concepts fundamental to a liberal arts math curriculum for 

even the most hesitant student. 

FEATURES 

MATHEMATICS IN OUR WORLD: these chapter openers show 

how mathematics is used in modern times. They introduce a scenario 

and a problem that is representative of the material that the upcoming 

chapter will cover. 

ABUNDANCE OF EXERCISES: A nice variety and quantity of 

exercises are provided. 

SIDELIGHTS: this feature contains various historical perspectives 

from biographies of famous mathematics figures to the development 

of mathematical topics. Sidelights also contain interesting topics 

that are not included in the body of the text. 

MATH NOTES: notes given in the margin provide suggestions 

on solving problems or more insight pertaining to presented concepts. 

CALCULATOR EXPLORATIONS: located throughout the text, 

they highlight topics and show how calculators may be used as tools 

to solve problems while reinforcing the presented material. 

CONTENTS 

Chapter 1: Problem Solving 

1-1 The Nature of Mathematical Reasoning 

1-2 Estimation and Interpreting Graphs 

1-3 Problem Solving 

Chapter 1 Review 

Chapter 2: Sets 

2-1 The Nature of Sets 

2-2 Subsets and Set Operations 

2-3 Venn Diagrams 

2-4 Using Sets to Solve Problems 

2-5 Infinite Sets 


Chapter 3: Logic 

3-1 Statements and Quantifiers 

3-2 Truth Tables 

3-3 Types of Statements 

3-4 Logical Arguments 

3-5 Euler Circles 


Chapter 4: Numeration Systems 

4-1 Early and Modern Numeration Systems 

4-2 Tools and Algorithms in Arithmetic 

4-3 Base Number Systems 

4-4 Operations in Base Number Systems 


Chapter 5: The Real Number System 

5-1 The Natural Numbers 

5-2 The Integers 

5-3 The Rational Numbers 

5-4 The Irrational Numbers 

5-5 The Real Numbers 

5-6 Exponents and Scientific Notation 

5-7 Arithmetic and Geometric Sequences 


Chapter 6: Topics in Algebra 

6-1 The Fundamentals of Algebra 

6-2 Solving Linear Equations 

6-3 Applications of Linear Equations 

6-4 Ratio, Proportion, and Variation 

6-5 Solving Linear Inequalities 

6-6 Solving Quadratic Equations 


Chapter 7: Additional Topics in Algebra 

7-1 The Rectangular Coordinate System and Linear Equations in 

Two Variables 

7-2 Systems of Linear Equations 

7-3 Solving Systems of Linear Equations Using Matrices 

7-4 Linear Inequalities 

7-5 Linear Programming 

7-6 Functions 

7-7 Linear, Quadratic, and Exponential Functions 

Supplement: An Application of Functions--Sound 


Chapter 8: Consumer Mathematics 

8-1 Percents 

8-2 Simple Interest 

8-3 Compound Interest 

44


8-4 Installment Buying 

8-5 Home Ownership 

8-6 Stocks and Bonds 



9-1 Measures of Length: Converting Units and the Metric System 

9-2 Measures of Area, Volume, and Capacity 

9-3 Measures of Weight and Temperature 


Chapter 10: Geometry 

10-1 Points, Lines, Planes and Angles 

10-2 Triangles 

10-3 Polygons and Perimeter 

10-4 Areas of Polygons and Circles 

10-5 Volume and Surface Area 

10-6 Right Triangle Trigonometry 

10-7 A Brief Survey of Non-Euclidean and Transformational Geometries 


Chapter 11: Probability and Counting Techniques 

11-1 The Fundamental Counting Rule and Permutations 

11-2 Combinations 

11-3 Basic Concepts of Probability 

11-4 Tree Diagrams, Tables, and Sample Spaces 

11-5 Probability Using Permutations and Combinations 

11-6 Odds and Expectation 

11-7 The Addition Rules for Probability 

11-8 The Multiplication Rules and Conditional Probability 

11-9 The Binomial Distribution 


Chapter 12: Statistics 

12-1 The Nature of Statistics and Organizing Data 

12-2 Picturing Data 

12-3 Measures of Average 

12-4 Measures of Variation 

12-5 Measures of Position 

12-6 The Normal Distribution 

12-7 Applications of the Normal Distribution 

12-8 Correlation and Regression Analysis 

Supplement: Misuses of Statistics 


Chapter 13: Other Mathematical Systems 

13-1 Mathematical Systems and Groups 

13-2 Clock Arithmetic 

13-3 Modular Systems 


Chapter 14: Voting Methods 

14-1 Preference Tables and the Plurality Method 

14-2 The Borda Count Method and the Plurality-with-Elimination 

Method 

14-3 The Pairwise Comparison Method and Approval Voting 

14-4 Apportionment 

14-5 Apportionment Flaws 


Chapter 15: Graph Theory 

15-1 Basic Concepts of Graph Theory 

15-2 Euler’s Theorem 

15-3 Hamilton Paths and Circuits 

15-4 Trees 


International edition 

APPLIED MATHEMATICS FOR BUSINESS, 

ECONOMICS AND THE SOCIAL SCIENCE 

4th Edition 

By Frank S. Budnick, University of Rhode Island 

1993 / 1,056 pages / Softcover 

ISBN: 9780070089020 (Out-of-Print) 

ISBN: 9780071125802 [IE] 

CONTENTS 

1 Some Preliminaries 

2 Linear Equations 


4 Functions and Graphs 

5 Linear Functionsand Applications 

6 Quadratic and Polynomial Functions 


8 Mathematics of Finance 

9 Matrix Algebra 

10 Linear ProgrammingAn Introduction 

11 The Simplex Method 

12 Trans-portation and Assignment Models 

13 Introduction to Probability Theory 

14 Probability Distributions 

15 Differentiation 

16 Optimization Methodology and Applications 

17 Integral Calculus An Introduction 

18 Integral CalculusApplications 

19 Optimization Functions of Several Variables 

Appendix A Review of Algebra 

SCHAUM’S OUTLINE OF MATHEMATICS 

FOR LIBERAL ARTS MAJORS 

By Christopher Thomas 

2009 (August 2008) / 240 pages 

ISBN: 9780071544290 


Schaum’s Outline of Mathematics for Liberal Arts Majors helps students 

understand basic concepts and offer extra practice on such 

topics as logic, truth tables, axiom statements, consumer mathematics, 

probability and counting techniques, the real number system, and 

more. Each chapter offers clear concise explanations of topics and 

include hundreds of practice problems with step-by-step solutions. 

CONTENTS 

1. Number Systems 

2. Sets 

3. Logic 

4. Fair Division 

5. Functions 

6. Geometry 

7. Graph Theory 

8. Financial Mathematics 



11. Weighted Voting 

12. Voting Methods 

13. Transformations and Symmetry 

14. Iterative Processes 

15. Trigonometry 

45


Mathematics for 

Elementary Teachers 

NEW *9780073519579* 

MATHEMATICS FOR 

ELEMENTARY TEACHERS 

A Conceptual Approach, 

9th Edition 

By Albert B Bennett, University of New Hampshire, 

Laurie J Burton, Western Oregon University 

and Ted Nelson, Portland State University 

2012 (January 2011) / 928 pages 

ISBN: 9780073519579 

www.mhhe.com/bbn 

The ninth edition of Mathematics for Elementary Teachers: A Conceptual 

Approach continues the innovative time-tested approach of 

 

examples and the extensive use of visual aids, hands-on activities, 

problem-solving strategies and active classroom participation. Features 

of the text focus on ensuring that prospective teachers will gain 

not only a deeper understanding of the mathematical concepts, but 

also a better sense of the connections between their college math 

courses and their future teaching experiences, along with helpful ideas 

for presenting math to their students in a way that will generate interest 

and enthusiasm. The text draws heavily on NCTM Standards and 

contains many pedagogical elements designed to foster reasoning, 

problem-solving and communication skills. 

 

online course management as roughly half of all problems in the 

text will be assignable through our new online homework platform, 

Connect Mathematics. In addition, Connect Mathematics will be fully 

integrated with Blackboard, providing the deepest integration of an online 

homework and course management system in the market today. 

Additionally, this text contains an activity set that corresponds to each 

section of the companion text, Mathematics for Elementary Teachers: 

An Activity Approach, also by the Bennett, Burton, and Nelson team. 

Mathematics for Elementary Teachers: An Activity Approach can be 

used independently or along with its companion, Mathematics for 

Elementary Teachers: A Conceptual Approach. 


Updated Elementary School Pages and Corresponding Questions: 

Sample elementary school text pages pulled from McGraw-Hill’s 

School Education Group’s books have been updated throughout the 

text to reflect their new series, Math Connects, a copyright 2009 series. 

This replaces many pages from a copyright 2005 series no longer in 

print and represents a critically acclaimed philosophical shift in the 

creation of elementary school texts. The Math Connects series has 

been created using NCTM Focal Points for each grade level as their 

guide to help create a more balanced plan of instruction that can 

accommodate a variety of instructional techniques. 

Revised and updated statistics, questions, and real-to-life applications: 

Throughout the text, statistics, questions, and real-to-life applications 

have been updated to ensure relevancy for today’s students. 

Revised and clarified diagrams: The authors have carefully reviewed 

all diagrams in the text and updated those that were unclear 

or outdated to ensure that all diagrams are both relevant and clear 

for students. 

Streamlined and clarified mathematical discussion: The presentation 

and word choice have been carefully examined by the authors 

to ensure the highest degree of clarity and relevance for students 

taking the course. 

Updates to the interior design: Revision to the interior design has 

improved both the aesthetic appeal as well as pedagogical usefulness 

throughout the text. Any extraneous use of color that might be viewed 

as distracting has been minimized and the dated use of gradated 

color on many elements has been removed in favor of bolder, more 

eye catching solid use of color. 

Connect Mathematics: For the first time, online homework and 

a full course management system will be available with the Bennett/ 

Burton/Nelson through McGraw-Hill’s new online system, Connect 

Mathematics. This new system will be fully integrated with Blackboard, 

providing the deepest level of integration between an online homework 

system and course management system. 

PowerPoint Presentations: In addition to the already popular 

online resources like the virtual manipulative kit, instructor’s resource 

manual, and interactive math applets; instructors will now have access 

to custom PowerPoint presentations. 

FEATURES 

Robust Exercise Sets: Skill and concept exercises appear in 

each section, with answers to odd-numbered problems provided 

in the back of the text. Special exercise types, in addition to those 

previously described, include calculator exercises, exercises that 

require the use of mental calculating and estimating techniques, and 

reasoning and problem solving exercises that reinforce Polya’s fourstep 

problem-solving approach. 

Worked-out examples appear throughout each section, providing 

students with a guided to solution on how to solve a problem. 

Problem Solving is emphasized through the text. Each section 

begins with a Problem Opener that poses an interesting problem to 

be solved and extended. Problem-Solving Applications in the sections 

utilize Polya’s four-step approach and one or more problem-solving 

strategies to analyze a problem related to the concepts in the section. 

Spotlight on Teaching: Each chapter opens with a Spotlight on 

Teaching segment that highlights a selection from the NCTM Standards 

that relates to the chapter content. 

Math Activities: A one-page Math Activity precedes every section 

in the text and provides opportunities for hands-on problem solving 

and group discussions. Most of the Math Activities involve emphasize 

the use of either the physical or Virtual Manipulatives. 

Companion Website: This site provides students with access to 

math applets, virtual manipulatives and many additional resources 

that help further their understanding of the material at no additional 

charge. From the companion website instructors have access to an 

Instructor’s Manual, editable exams, planning guides and much more. 

CONTENTS 


1.1 Introduction to Problem Solving 

1.2 Patterns and Problem Solving 

1.3 Problem Solving with Algebra 

Chapter 2: Sets, Functions, and Reasoning 

2.1 Sets and Venn Diagrams 

2.2 Functions, Coordinates, and Graphs 

2.3 Introduction to Deductive Reasoning 


3.1 Numeration Systems 



3.4 Division and Exponents 

Chapter 4: Number Theory 

4.1 Factors and Multiples 

4.2 Greatest Common Factor and Least Common Multiple 

46


Chapter 5: Integers and Fractions 

5.1 Integers 


5.3 Operations with Fractions 

Chapter 6: Decimals: Rational and Irrational Numbers 

6.1 Decimals and Rational Numbers 

6.2 Operations with Decimals 

6.3 Ratio, Percent, and Scientific Notation 

6.4 Irrational and Real Numbers 


7.1 Collecting and Graphing Data 

7.2 Describing and Analyzing Data 

7.3 Sampling, Predictions, and Simulations 

Chapter 8: Probability 

8.1 Single-Stage Experiments 

8.2 Multistage Experiments 

Chapter 9: Geometric Figures 

9.1 Plane Figures 

9.2 Polygons and Tessellations 

9.3 Space Figures 

9.4 Symmetric Figures 


10.1 Systems of Measurement 

10.2 Area and Perimeter 

10.3 Volume and Surface Area 

Chapter 11: Motions in Geometry 

11.1 Congruence and Constructions 

11.2 Congruence Mappings 

11.3 Similarity Mappings 

References for Research Statements by Chapter 

Answers to Selected Math Activities 

Answers to Odd-Numbered Exercises and Problems and Chapter 

Tests 

NEW *9780077430917* 

MATHEMATICS FOR 

ELEMENTARY TEACHERS 

An Activity Approach, 

9th Edition 

By Albert B. Bennett, Univ of New Hampshire, 

Ted Nelson, Portland State University and Laurie 

J. Burton, Western Oregon University 

2012 (January 2011) / 416 pages 

ISBN: 9780077430917 

www.mhhe.com/bbn 

The primary purpose of Mathematics for Elementary Teachers: An 

Activity Approach is to engage prospective elementary and middleschool 

teachers in mathematical activities that will enhance their 

conceptual knowledge, introduce them to important manipulatives, 

and model the kind of mathematical learning experiences they will 

be expected to provide for their students. The activities incorporate 

inductive thinking and the use of physical models and visual images 

to develop concepts and encourage higher-level reasoning. The 

Activity Approach contains Activity Sets that correspond to each 

section of the text and augment the ideas presented in the sections. 

Each Activity Set consists of a sequence of inductive activities and 

experiments that enable the student to build an understanding of 

mathematical ideas through the use of models and the discovery 

of patterns. In addition, over thirty Material Cards are included that 

complement the color cardstock materials in the Manipulative Kit. A 

section on Ideas for the Elementary Classroom at the end of each 

chapter includes a suggested Elementary-School Activity that has 

been adapted from one of the chapter’s Activity Sets. Additionally, a 

companion text, Mathematics for Elementary Teachers: A Conceptual 

Approach, is also available from the Bennett, Burton, and Nelson 

team. Mathematics for Elementary Teachers: A Conceptual Approach 

can be used independently or along with Mathematics for Elementary 

Teachers: An Activity Approach. 


Updated Elementary School Pages and Corresponding Questions: 

Sample elementary school text pages pulled from McGraw-Hill’s 

School Education Group’s books have been updated throughout the 

text to reflect their new series, Math Connects, a copyright 2009 series. 

This replaces many pages from a copyright 2005 series no longer in 

print and represents a critically acclaimed philosophical shift in the 

creation of elementary school texts. The Math Connects series has 

been created using NCTM Focal Points for each grade level as their 

guide to help create a more balanced plan of instruction that can 

accommodate a variety of instructional techniques. 

Revised and updated statistics, questions, and real-to-life applications: 

Throughout the text, statistics, questions, and real-to-life applications 

have been updated to ensure relevancy for today’s students. 

Revised and clarified diagrams: The authors have carefully reviewed 

all diagrams in the text and updated those that were unclear 

or outdated to ensure that all diagrams are both relevant and clear 

for students. 

Streamlined and clarified mathematical discussion: The presentation 

and word choice have been carefully examined by the authors 

to ensure the highest degree of clarity and relevance for students 

taking the course. 

Updates to the interior design has improved both the aesthetic 

appeal as well as pedagogical usefulness throughout the text. Any 

extraneous use of color that might be viewed as distracting has been 

minimized and the dated use of gradated color on many elements has 

been removed in favor of bolder, more eye catching solid use of color. 

PowerPoint Presentations: In addition to the already popular 

online resources like the virtual manipulative kit, instructor’s resource 

manual, and interactive math applets; instructors will now have access 

to custom PowerPoint presentations. 

FEATURES 

Discovery Based Activity Sets: Each Activity Set uses materials 

and/or visual models to provide a context for understanding. The 

questions and activities in each Activity Set are sequentially developed 

to encourage discovery and to provide an in-depth exploration for a 

topic. Students are asked to describe patterns, form conjectures, look 

for relationships, and discuss their thinking. 

Manipulative Kit: Manipulatives designed for use with each Activity 

Set (and selected Follow–Up Questions and Activities) can be 

packaged with Math for Elementary Teachers: An Activity Approach. 

A Manipulative Kit holds resealable, labeled bags for each type of 

manipulative. 

Follow-Up Questions and Activities: Follow-Up Questions and 

Activities at the end of each Activity Set ask students to relate the 

activity set to three important areas: connections to the elementary 

classroom, related mathematics concepts, and the NCTM Standards 

and Expectations from the Principle and Standards for School 

Mathematics. 

NCTM Standards and Expectations: A durable, removable 

cardstock table of the NCTM Standards and Expectations for Grades 

Pre-K – 2, 3 – 5, and 6 – 8 is provided in the back of the book so students 

can answer end of section Follow-Up Questions and Activities 

and see what mathematics is recommended at various grade levels. 

CONTENTS 


1.1 Introduction to Problem Solving 

1.2 Patterns and Problem Solving 

1.3 Problem Solving with Algebra 

Chapter 2: Sets, Functions, and Reasoning 

47


2.1 Sets and Venn Diagrams 

2.2 Functions, Coordinates, and Graphs 

2.3 Introduction to Deductive Reasoning 


3.1 Numeration Systems 



3.4 Division and Exponents 


4.1 Factors and Multiples 

4.2 Greatest Common Factor and Least Common Multiple 

Chapter 5: Integers and Fractions 

5.1 Integers 


5.3 Operations with Fractions 

Chapter 6: Decimals: Rational and Irrational Numbers 

6.1 Decimals and Rational Numbers 

6.2 Operations with Decimals 

6.3 Ratio, Percent, and Scientific Notation 

6.4 Irrational and Real Numbers 


7.1 Collecting and Graphing Data 

7.2 Describing and Analyzing Data 

7.3 Sampling, Predictions, and Simulations 


8.1 Single-Stage Experiments 

8.2, 8.2 Multistage Experiments 

Chapter 9: Geometric Figures 

9.1 Plane Figures 

9.2 Polygons and Tessellations 

9.3 Space Figures 

9.4 Symmetric Figures 


10.1 Systems of Measurement 

10.2 Area and Perimeter 

10.3 Volume and Surface Area 

Chapter 11: Motions in Geometry 

11.1 Congruence and Constructions 

11.2 Congruence Mappings 

11.3 Similarity Mappings 

References for Research Statements by Chapter 

Answers to Selected Math Activities 

Answers to Odd-Numbered Exercises and Problems and Chapter 

Tests 

All Global Editions are 

adapted to better meet the 

needs of courses outside 

the United States. 

Please contact your local 

sales representative for 

more details. 

Discrete Mathematics 

Global edition 

NEW *9780073383095* 

DISCRETE MATHEMATICS AND ITS 

APPLICATIONS 

7th Edition 

By Kenneth H Rosen, Visiting Research Professor, Monmouth University- 

New Jersey 

2012 (June 2011) / 1024 pages 

ISBN: 9780073383095 

ISBN: 9780071317108 [GE] - March 2012 

www.mhhe.com/rosen 

Discrete Mathematics and its Applications, Seventh Edition, is intended 

for one- or two-term introductory discrete mathematics courses 

taken by students from a wide variety of majors, including computer 

science, mathematics, and engineering. This renowned best-selling 

text, which has been used at over 500 institutions around the world, 

gives a focused introduction to the primary themes in a discrete 

mathematics course and demonstrates the relevance and practicality 

of discrete mathematics to a wide a wide variety of real-world applications…from 

computer science to data networking, to psychology, to 

chemistry, to engineering, to linguistics, to biology, to business, and 

 


Improved Introduction and Organization - For the seventh edition 

the first part of the book has been restructured to present core topics 

in a more efficient, more effective, and more flexible way. 

Expanded and Improved Coverage - The seventh edition offers 

brand-new or expanded coverage in several key areas to present 

important topics with better care, detail, and flexibility. 

FEATURES 

Exercises – There are over 3800 exercises in the text, from 

straightforward problems that develop basic skills to a large number 

of intermediate and challenging exercises. Exercise sets also contain 

special discussions that develop new concepts not covered in the 

text, enabling students to discover new ideas through their own work. 

Worked Examples – Over 750 examples are used to illustrate 

concepts, relate different topics, and introduce applications. Over 200 

are new to this edition. 

Historical Information – The background of many topics are 

succinctly described in the text using historical footnotes and brief 

biographies of more than 65 mathematicians and computer scientists 

who were (and are) important contributors to discrete mathematics. 

Clarity and Precision – Rosen’s writing style is direct and pragmatic. 

Precise mathematical language is used without excessive 

formalism and abstraction. Care has been taken to balance the mix 

of notation and words in mathematical statements. 

Flexible Organization – The dependence of chapters on previous 

material has been minimized to allow instructors flexibility to pick and 

choose topics. Each chapter is divided into sections of approximately 

the same length, and each section is divided into subsections that 

form natural blocks of material for teaching. Instructors can easily 

pace their lectures using these blocks. 

Accessibility – This text has proven to be easy to read and understand 

by beginning students. There are no mathematical prerequisites 

beyond college algebra for almost all of this text, and the few places 

in the book where calculus is referred to are explicitly noted. 

48


• Now over 400 Extra Examples covering all chapters of the text 

• 14 new and revised Self-Assessments, interactive guides to assess 

understanding of key concepts 

• An expanded number of Interactive Demonstration Applets for 

interactively exploring how important algorithms work 

• An updated Web Resources Guide containing new links to hundreds 

of external websites relevant to the text material. 

• An updated Exploring Discrete Mathematics with Maple guide 

featuring new material tied to the text and full compatibility with 

Maple 10 

• An updated Applications of Discrete Mathematics supplement 

containing in-depth explorations of applications, with exercises 

and projects 

• Additional instructor resources for in-class use, such as printable 

tests, image banks, lecture notes, and materials donated by our 

community of users 

CONTENTS 

Chapter 1: The Foundations: Logic and Proofs 

Chapter 2: Basic Structures: Sets, Functions, Sequences, Sums, 

Matrices 

Chapter 3: Algorithms 


Chapter 5: Induction and Recursion 

Chapter 6: Counting 

Chapter 7: Discrete Probability 

Chapter 8: Advanced Counting Techniques 

Chapter 9: Relations 

Chapter 10: Graphs 

Chapter 11: Trees 

Chapter 12: Boolean Algebra 

Chapter 13: Modeling Computation 

Appendices 

SCHAUM’S OUTLINE OF DISCRETE 

MATHEMATICS 

Revised 3rd Edition 

By Seymour Lipschutz, Temple University-Philadelphia and Marc Lipson, 

University of Georgia 

2010 (August 2009) / 496 pages / Softcover 

ISBN: 9780071615860 


Discrete mathematics becomes more and more important as the 

digital age goes forward. This newly revised third edition updates all 

areas of the subject. 

CONTENTS 

Set Theory 

Relations 

Functions and Algorithms 

Logic and Propositional Calculus 

Counting 

Advanced Counting Techniques 

Computer Arithmetic 

Probability Theory 

Graph Theory 

Directed Graphs 

Binary Trees 

Properties of the Integers 

Cryptology 

Languages, Grammar, Machines 

Ordered Sets and Lattices 

Boolean Algebra 

Appendix A: Vectors and Matrices 

Appendix B: Algebraic Systems 

SCHAUM’S 2,000 SOLVED PROBLEMS IN 

DISCRETE MATHEMATICS 

By Seymour Lipschutz, Temple University 

1992 / 412 pages 

ISBN: 9780070380318 

ISBN: 9780071126908 [IE] - (Out of Print) 


(International Edition is not for sale in Japan.) 

CONTENTS 

Set Theory. 

Relations. 

Functions. 

Vectors and Matrices. 

Graph Theory. 

Planar Graphs and Trees. 

Directed Graphs and Binary Trees. 

Combinatorial Analysis. 

Algebraic Systems. 

Languages, Grammars, Automata. 

Ordered Sets and Lattices. 

Propositional Calculus. 

Boolean Algebra. 

Logic Gates. 

SCHAUM’S OUTLINE OF BOOLEAN 

ALGEBRA AND SWITCHING CIRCUITS 

By Elliott Mendelson, Queens College 

1970 / 224 pages 

ISBN: 9780070414600 


CONTENTS 

The Algebra of Logic 

The Algebra of Sets 

Boolean Algebras 

Switching Circuits and Logic Circuits 

Topics in the Theory of Boolean Algebras 

Appendix 

REVIEW COPY 










49


Technical Mathematics 

MATHEMATICS FOR TECHNICIANS 

6th Edition 

By Blair Alldis, Randwick College of TAFE 


ISBN: 9780070131651 

(McGraw-Hill Australia Title) 

Mathematics for Technicians 6th Edition remains the leading Australian 

text for students studying Mathematics, including Engineering 

Maths A and Engineering Maths B. This edition uses a building block 

approach with worked examples, banks of exercises for each section, 

and self-test questions ideal for revision and exam preparation. 

Answers to questions in the text are located at the back of the book. 


Mathematical rules, advice, notes and definitions are highlighted 

for added emphasis 

Exercises, self-test questions and extra activities on the CD 

provide students with a range of revision and comprehension tools 

Chapter summaries, worked examples and diagrams aid student 

comprehension 

A CD is included with the book which contains extra theory, 

exercises and answers. 


SCHAUM’S OUTLINE OF INTRODUCTION TO 

MATHEMATICAL ECONOMICS 

Revised 3rd Edition 

By Edward T Dowling, Fordham University 


ISBN: 9780071762519 


Schaum’s Outline of Mathematical Economics mirrors the courses 

in scope and sequence to help enrolled students understand basic 

concepts and offer extra practice on topics such as multivariable functions, 

exponential and logarithmic functions, matrix inversion, linear 

algebra, and differential and difference equations. 

CONTENTS 

1. Review 

2. Economic Applications of Graphs and Equations 

3. The Derivative and the Rules of Differentiation. 

4. Uses of the Derivative in Mathematics and Economics 

5. Calculus of Multivariable Functions 

6. Calculus of Multivariable Functions in Economics 

7. Exponential and Logarithmic Functions in Economics 

8. Differentiation of Exponential and Logarithmic Functions 

9. The Fundamentals of Linear (or Matrix) Algebra 

10. Matrix Inversion 

11. Special Determinants and Matrices and Their Use in Economics 

12. Comparative Statics and Concave Programming 

13. IUntegral Calculus: The Indefinite Integral 

14. Integral Calculus: The Definite Integral 

15. First-Order Differential Equations 

16. First Order Difference Equations 

17. Second-Order Differential Equations and Difference Equations 

18. Simultaneous Differential and Difference Equations 

19. The Calculus of Variations 

20. Optimal Control Theory 


METHODS FOR BUSINESS AND 

ECONOMICS 

By Edward T. Dowling, Fordham University 

2010 (August 2009) / 408 pages 

ISBN: 9780071635325 


Schaum’s Outline of Mathematical Methods for Business and Economics 

reviews the mathematical tools, topics, and techniques essential 

for success in business and economics today. The theory and solved 

problem format of each chapter provides concise explanations illustrated 

by examples, plus numerous problems with fully worked-out 

solutions. And you don’t have to know advanced math beyond what 

you learned high school. The pedagogy enables you to progress at 

your own pace and adapt the book to your own needs. 

FEATURES 

 

1066 fully solved problems 

Clear, concise explanations of all mathematical concepts for 

business and economics 

 

Covers all course fundamentals 

Appropriate for the following courses: Calculus for Business, Applied 

Calculus, Calculus for Social Sciences, Calculus for Economics 

CONTENTS 

1. Review 

2. Equations and Graphs 

3. Functions 

4. Systems of Equations 

5. Linear (or Matrix) Algebra 

6. Solving Linear Equations with Matrix Algebra 

7. Linear Programming: Using Graphs 

8. Linear Programming: The Simplex Algorithm and the Dual 

9. Differential Calculus: The Derivative and the Rules of Differentiation 

10. Differential Calculus: Uses of the Derivative 

11. Exponential and Logarithmic Functions 

12. Integral Calculus 

13. Calculus of Multivariable Functions 




 




50


SUPERSYMMETRY DEMYSTIFIED 

by Patrick LaBelle 


ISBN: 9780071636414 

 

complex topic of supersymmetry--a key tool in most cutting-edge research 

in particle physics, including superstring theory. The book uses 

 

them as the chapters progress. Hundreds of worked equations and 

examples make it easy to understand the material, and end-of-chapter 

 

CONTENTS 

Chapter 1. Introduction; 

Chapter 2. A Crash Course on Weyl Spinors; 

Chapter 3. New Notation for the Components of Weyl Spinors; 

Chapter 4. The Physics of Weyl, Majorana, and Dirac Spinors; 

Chapter 5. Building the Simplest Supersymmetric Lagrangian; 

Chapter 6. The Supersymmetric Charges and Their Algebra; 

Chapter 7. Applications of the SUSY Algebra; 

Chapter 8. Adding Interactions: The Wess-Zumino Model; 

Chapter 9. Some Explicit Calculations; 

Chapter 10. Supersymmetric Gauge Theories; 

Chapter 11. Superspace Formalism; 

Chapter 12. Left-Chiral Superfields; 

Chapter 13. Supersymmetric Gauge Field Theories in the Superfield 

Approach; 

Chapter 14. SUSY Breaking; 

Chapter 15. Introduction to the Minimal Supersymmetric Standard 

Model; 

Chapter 16. Some Phenomenological Implications of the MSSM; 

Final Exam; 

Appendix A. Useful Identities; 

Appendix B. Solutions to Exercises; 

Appendix C. Solutions to Quizzes; 

Appendix D. Solutions to Final Exam; 

Index 

SCHAUM’S OUTLINE OF BASIC BUSINESS 

MATHEMATICS 

2nd Edition 

by Eugene Don, and Joel J. Lerner, Sulivan County Community College 


ISBN: 9780071611589 


Schaum’s Outline of Basic Business Mathematics helps beginning 

business students learn the practical application of mathematical 

concepts used in the business world, including stock market applications, 

appreciation rates, and averaging inventory controls. 

This book differs from Schaum’s Outline of Business Mathematics 

in that it focuses exclusively on business (rather than business and 

 

course fundamentals in easy-to-understand language with illustrative 

examples. The outline supplements business mathematics texts and 

is best suited to two-year college business courses. 

CONTENTS 

Review of Arithmetic. 

Ratio, Proportion, and Percent. 

Payroll. 

Depreciation. 

Interest and Discount. 

Annuities and Their Applications. 

Stocks and Bonds. 

Buying. 

Selling. 

Insurance. 

Introduction to Statistics. 

SCHAUM’S OUTLINE OF BASIC 

MATHEMATICS WITH APPLICATIONS TO 

SCIENCE AND TECHNOLOGY 

2nd Edition 

by Haym Kruglak Ph.D., Western Michigan University, John T. Moore 

(deceased), and Ramon A. Mata-Toledo, James Madison University 


ISBN: 9780071611596 


This classic outline provides practical applications of basic mathematics 

for science, technology, and astronomy students. Each chapter 

 

with illustrative examples. The new edition will add new material to the 

 

introduce the use of calculators for arithmetic operations; and provide 

a new chapter on descriptive statistics. 

CONTENTS 

1. Decimal Fractions 

2. Measurement and Scientific Notation 

3. Common Fractions 

4. Percentage 

5. Essentials of Algebra 

6. Ratio and Proportion 

7. Linear Equations 

8. Exponents and Radicals 

9. Logarithms 

10. Quadratic Equations and Square Roots 

11. Essentials of Plane Geometry 

12. Solid Figures 

13. Trigonometric Figures 

14. Solution of Triangles 

15. Vectors 

16. Radian Measure 


18. Numbering Systems 

19. Arithmetic Operations in a Computer 

20. Counting Methods 

21. Probability and Odds 


MASTERING TECHNICAL MATHEMATICS 

3rd Edition 

By Stan Gibilisco and Norman H. Crowhurst (deceased) 

2008 / 627 pages 

ISBN: 9780071494489 


 

 

 

wishing to boost their career by learning the principles of mathematics 

as they apply to science and engineering. Featuring the same 

user-friendly pedagogy, practical examples, and detailed illustrations 

 

communities, the new third edition delivers four entirely new chapters 

and expanded treatment of cutting-edge topics. 

CONTENTS 

PART 1: WORKING WITH NUMBERS 

Ch 1. From Counting to Addition 

Ch 2. Subtraction 

Ch 3. Multiplication 

Ch 4. Division 

Ch 5. Fractions 

Ch 6. Area and Volume 

Ch 7. Time as a Dimension 

51


PART 2: ALGEBRA, GEOMETRY, AND TRIGONOMETRY 

Ch 8. First Notions in Algebra 

Ch 9. “School” Algebra 

Ch 10. Quadratic Equations 

Ch 11. Some Useful Shortcuts 

Ch 12. Mechanical Mathematics 

Ch 13. Ratio and Proportion 

Ch 14. Trigonometric and Geometric Calculations 

PART 3: ANALYSIS AND CALCULUS 

Ch 15. Systems of Counting 

Ch 16. Theory of Progressions 

Ch 17. Practical Progressions 

Ch 18. Analyzing Motion 

Ch 19. Developing Calculus Theory 

Ch 20. Combining Calculus with Other Tools 

Ch 21. Coordinate Systems and Graphs 

Ch 22. Imaginary and Complex Numbers 

PART 4: TOOLS OF APPLIED MATHEMATICS 

Ch 23. Working with Series 

Ch 24. Logarithms 

Ch 25. Handy Formulas and Techniques 

Ch 26. Calculation Aids 

Ch 27. Digital Mathematics 

Ch 28. Vector Quantities 

Ch 29. Scientific Notation 

Ch 30. Working with Statistics 

TECHNICAL MATH DEMYSTIFIED 


2006 / 412 pages 

ISBN: 9780071459495 

(A Professional Reference) 

CONTENTS 

PREFACE 

ACKNOWLEDGMENTS 

Chapter 1: Numbering Systems 

Chapter 2: Principles of Calculation 

Chapter 3: Specific Notation 

Chapter 4: Coordinates in Two Dimensions 

Chapter 5: Coordinates in Three Dimensions 

Chapter 6: Equations in One Variable 

Chapter 7: Multivariable Equations 

Chapter 8: Perimeter and Area in Two Dimensions 

Chapter 9: Surface Area and Volume in Three Dimensions 

Chapter 10: Boolean Algebra 

Chapter 11: Trigonometric Functions 

Chapter 12: Vectors in Two and Three Dimensions 

Chapter 13: Logarithmic and Exponential Functions 

Chapter 14: Differentiation in One Variable 

Chapter 15: Integration in One Variable 

FINAL EXAM 

ANSWERS TO QUIZ AND EXAM QUESTIONS 


INDEX 

SCHAUM’S OUTLINE OF BEGINNING FINITE 

MATHEMATICS 

By Seymour Lipschutz , Temple University -Philadelphia; John J Schiller 

and R. Alu Srinivasan, Temple University 


ISBN: 9780071388979 


Most colleges and universities now require their non-science majors to 

take a one- or two-semester course in mathematics. Taken by 300,000 

 

revised to match the structures and syllabuses of contemporary course 

offerings, Schaum’s Outline of Beginning Finite Mathematics provides 

a thorough review-- with worked examples--of the fundamentals of 

linear equations and linear growth. Topics covered include games 

theory, descriptive statistics, normal distribution, probability, binomial 

distribution, and voting systems and apportionment. 

SCHAUM’S OUTLINE OF MATHEMATICS 

FOR NURSES 

By Larry Stephens, University of Nebraska, Lana C Stephens and Eizo 

Nishiura, Queensborough Community College 

2003 / 256 pages 

ISBN: 9780071400220 


A review of basic arithmetic precedes clear explanations of how nurses 

need to apply mathematics in modern clinical practice. This study 

guide teaches an especially easy approach to solving the proportion 

problems key to converting medication orders and passing nursing 

licensing exams. The profusion of problems with detailed solutions, 

and hundreds more with answers, gives students ample opportunities 

to test their skills as they learn them--leading to quicker mastery. 



3rd Edition 


2001 / 523 pages 

ISBN: 9780071358965 

ISBN: 9780071188715 [IE] (Out-of Print) 


CONTENTS 

Review. 

Economic Applications of Graphs and Equations. 

The Derivative and the Rules of Differentiation. 

Uses of the Derivative in Mathematics and Economics. 

Calculus of Multivariable Functions. 

Caculus of Multivariable Functions in Economics. 

Exponential and Logarithmic Functions in Economics. 

Differentiation of Exponential and Logarithmic Functions. 

The Fundamentals of Linear (or Matrix) Algebra. 

Matrix Inversion. 

Special Determinants and Matrices and Their Use in Economics. 

Comparative Statics and Concave Programming. 

IUntegral Calculus: The Indefinite Integral. 

Integral Calculus: The Definite Integral. 

First-Order Differential Equations. 

First Order Difference Equations. 

Second-Order Differential Equations and Difference Equations. 

Simultaneous Differential and Difference Equations. 

The Calculus of Variations. 

Optimal Control Theory. 

52


SCHAUM’S OUTLINE OF BASIC 

MATHEMATICS FOR ELECTRICITY AND 

ELECTRONICS 

By Arthur Beiser, Formerly New York University 

1993 / 224 pages 

ISBN: 9780070044395 


CONTENTS 

Basic Electricity and Algebra. 

Fractions, Decimals, and Percentage. 

Power and Energy. 

Powers of 10 and Logarithms. 

Resistance and Wire Size. 

Series Circuits. 

Parallel Circuits. 

Simultaneous Equations and Kirchhoff’s Rules. 

Network Theorems. 

Inductance. 

Capacitance. 

Trigonometry and Vectors. 

Alternating Current. 

American Wire Gage Tables. 

Appendices: A: Conversion Factors. 

B: American Wire Gage Tables. 

C: Table of Allowable Current Carrying Capacities (ampacities) of 

Copper Conductors. 

D: Four-Place Logarithms. 

E: Natural Trigonometric Functions. 

Finite Mathematics 

SCHAUM’S OUTLINE OF BEGINNING FINITE 

MATHEMATICS 

By Seymour Lipschutz, Temple University-Philadelphia, John J Schiller 

and R Alu Srinivasan of Mathematics Department, Tenple 

2005 / 368 pages 

ISBN: 9780071388979 


Most colleges and universities now require their non-science majors to 

take a one- or two-semester course in mathematics. Taken by 300,000 

 

revised to match the structures and syllabuses of contemporary course 

offerings, Schaum’s Outline of Beginning Finite Mathematics provides 

a thorough review-- with worked examples--of the fundamentals of 

linear equations and linear growth. Topics covered include games 

theory, descriptive statistics, normal distribution, probability, binomial 

distribution, and voting systems and apportionment. 

SCHAUM’S EASY OUTLINE OF COLLEGE 

MATHEMATICS 

By Frank Ayres (deceased) and Philip Schmidt, State University of NY 

2001 / 138 pages 

ISBN: 9780071369756 


CONTENTS 

Chapter 1: Fundamentals of Algebra. 

Chapter 2: Functions and Equations. 

Chapter 3: Progressions, Sequences, and Series. 

Chapter 4: Permutations, Combinations, and Probability. 

Chapter 5: Systems of Linear Equations Using Determinants. 

Chapter 6: Trigonometry. 

Chapter 7: Introduction to Calculus. 

Business Mathematics 

SOLVING BUSINESS PROBLEMS USING A 

CALCULATOR STUDENT TEXT 

6th Edition 

By Mildred Polisky 

2003 / 288 pages 

ISBN: 9780078300202 

CONTENTS 

Contents 

Section 1 10-Key Touch Method 

Lesson 1 Touch Addition of Whole Numbers 

Lesson 2 Touch Addition and Subtraction of Whole Numbers 

Lesson 3 Crossfooting 

Lesson 4 Touch Addition and Subtraction of Dollars and Cents 

Lesson 5 Rounding and Estimating Without a Calculator 

Lesson 6 Multiplication 

Lesson 7 Division 

Business Calculator Applications 1: Keypad Introduction 

Practice Test 1 

Section 2 Multiplication and Division 

Lesson 8 Constant Multiplication and Division 

Lesson 9 Multiplying Three or More Factors 

Lesson 10 Mixed Operations 

Lesson 11 Accumulative Multiplication 

Lesson 12 Negative Multiplication 

Business Calculator Applications 2: Using Memory Keys for Repeated 

Operations 


Section 3 Percents and Discounts 

Lesson 13 Fractions and Decimals 

Lesson 14 Percents 

Lesson 15 Finding Percentage, Rate, and Base 

Lesson 16 Amounts and Percents of Increase or Decrease 

Lesson 17 Single Discounts 

Lesson 18 Series Discounts 

Lesson 19 Extending Invoices and Quantity Pricing 

Lesson 20 Auditing Invoices 

Business Calculator Applications 3: Percent of Change, The Percentage 

Formula, and Discounts 


Section 4 Retail Calculations and Payroll 

Lesson 22 Markdown 

Lesson 23 Monthly and Semimonthly Payrolls 

53


Lesson 24 Payrolls for Hourly Workers 

Lesson 25 Commission Payroll Plans 

Business Calculator Applications 4: Retail Calculations 


Section 5 Stocks and Bonds 

Lesson 27 Investments in Bonds 

Lesson 28 Yields on Investments 

Lesson 29 Selling Price of Stocks 

Business Calculator Applications 5: Prices of Treasury Bonds and 

Notes 


Section 6 Interest and the Metric System 

Lesson 30 Interest and Mortgage Interest 

Lesson 31 True Annual Interest Rate 

Lesson 32 Installment Buying 

Lesson 33 Prorating 

Lesson 34 Measurement 

Business Calculator Applications 6: Interest and Proration 


Progress Tests 

Answer Tabs 


BUSINESS MATH DEMYSTIFIED 

By Allan Bluman 

2006 / 390 pages 

ISBN: 9780071464703 

CONTENTS 

PREFACE 

Chapter 1: Fractions--Review 

Chapter 2: Decimals--Review 

Chapter 3: Percent--Review 

Chapter 4: Formulas--Review 

Chapter 5: Checking Accounts 

Chapter 6: Payroll and Commission 

Chapter 7: Markup 

Chapter 8: Discounts 

Chapter 9: Simple Interest and Promissory Notes 

Chapter 10: Compound Interest 

Chapter 11: Annuities and Sinking Funds 

Chapter 12: Consumer Credit 

Chapter 13: Mortgages 

Chapter 14: Insurance 

Chapter 15: Taxes 

Chapter 16: Stocks and Bonds 

Chapter 17: Depreciation 

Chapter 18: Inventory 

Chapter 19: Financial Statements 


Chapter 21: Charts and Graphs 

FINAL EXAM 

ANSWERS TO QUIZZES AND FINAL EXAM 

INDEX 

SCHAUM’S EASY OUT LINE OF 

INTRODUCTION TO MATHEMATICAL 

ECONOMICS 

By Edward Dowling 

2006 / 160 pages 

ISBN: 9780071455343 


When you are looking for a quick nuts-and-bolts overview, there’s 

no series that does it better. Schaum’s Easy Outline of Introduction 

 

focused version of its predecessor. 



3rd Edition 


2001 / 523 pages 

ISBN: 9780071358965 

ISBN: 9780071188715 [IE] (Out-of Print) 


CONTENTS 

Review. 

Economic Applications of Graphs and Equations. 

The Derivative and the Rules of Differentiation. 

Uses of the Derivative in Mathematics and Economics. 

Calculus of Multivariable Functions. 

Caculus of Multivariable Functions in Economics. 

Exponential and Logarithmic Functions in Economics. 

Differentiation of Exponential and Logarithmic Functions. 

The Fundamentals of Linear (or Matrix) Algebra. 

Matrix Inversion. 

Special Determinants and Matrices and Their Use in Economics. 

Comparative Statics and Concave Programming. 

IUntegral Calculus: The Indefinite Integral. 

Integral Calculus: The Definite Integral. 

First-Order Differential Equations. 

First Order Difference Equations. 

Second-Order Differential Equations and Difference Equations. 

Simultaneous Differential and Difference Equations. 

The Calculus of Variations. 

Optimal Control Theory. 

SCHAUM’S OUTLINE OF MATHEMATICS OF 

FINANCE 

2nd Edition 

By Petr Zima and Robert Brown, University of Waterloo 

1996 / 304 pages 

ISBN: 9780070082038 


 

this book includes new material on life insurance, life annuities and 

more. Students learn how to master effective problem-solving techniques 

with 1,224 practice problems and questions. The large number 

and variety of practical applications offer a feel for how to conduct 

 

problems offer the opportunity for more study or self-testing 

54

College Algebra ..................................................................................................57 


College Algebra with Trigonometry .....................................................................64 

Precalculus .........................................................................................................67 


Trigonometry ......................................................................................................62 


PRECALCULUS 

55

New Titles 

PRECALCULUS 


College Algebra: Graphs and Models Coburn 9780073519548 57 

Precalculus: Graphs and Models Coburn 9780073519531 67 

PRECALCULUS 


College Algebra, 9e Barnett 9780077350161 58 

College Algebra with Trigonometry, 9e Barnett 9780077350109 64 

Precalculus, 7e Barnett 9780077349912 69 

Trigonometry, 2e Coburn 9780077349974 62 

56

Precalculus 

College Algebra 

NEW *9780073519548* 

COLLEGE ALGEBRA 

Graphs and Models 

By John Coburn, Saint Louis CC-Flors Valley 

and JD (John) Herdlick, Saint Louis CC-Meramec-Kirkwood 


ISBN: 9780073519548 

www.mhhe.com/coburn 

Three components contribute to a theme sustained throughout the 

 

solid framework, and providing strong connections. In the Graphs 

and Models texts, the authors combine their depth of experience 

with the conversational style and the wealth of applications that 

the Coburn-Herdlick texts have become known for. By combining 

a graphical approach to problem solving with algebraic methods, 

students learn how to relate their mathematical knowledge to the 

outside world. The authors use technology to solve the more true-to 

life equations, to engage more applications, and to explore the more 

 

feedback of hundreds of instructors and students across the country, 

College Algebra: Graphs & Models emphasizes connections in order 

to improve the level of student engagement in mathematics and 

increase their chances of success in college algebra. The launch of 

 

leap forward in terms of online course management with McGraw- 

Hill’s new homework platform, Connect Math Hosted by ALEKS 

Corp. Math instructors served as digital contributors to choose the 

problems that will be available, authoring each algorithm and providing 

stepped out solutions that go into great detail and are focused 

on areas where students commonly make mistakes. From there, the 

ALEKS Corporation reviewed each algorithm to ensure accuracy. A 

unifying theme throughout the entire process was the involvement of 

the authors. Through each step, they provided feedback and guidance 

to the digital contributors to ensure that the content being developed 

digitally closely matched the textbook. The result is an online homework 

platform that provides superior content and feedback, allowing 

students to effectively learn the material being taught. 

FEATURES 

ALEKS (Assessment and LEarning in Knowledge Spaces) – 

ALEKS is a Web-based, artificially intelligent assessment and learning 

system. ALEKS uses adaptive questioning to quickly and accurately 

determine exactly what a student knows and doesn’t know in a course. 

ALEKS then instructs the student on the topics she is most ready to 

learn. As a student works through a course, ALEKS periodically reassesses 

the student to ensure that topics learned are also retained. 

ALEKS courses are very complete in their topic coverage and ALEKS 

avoids multiple-choice questions. A student who shows a high level of 

mastery of an ALEKS course will be successful in the actual course 

he or she is taking. 

ALEKS also provides the advantages of one-on-one instruction, 

24/7, from virtually any Web-based computer for a fraction of the cost 

of a human tutor. 

ALEKS 360 offers a cost-effective total course solution by 

providing powerful ALEKS personalized assessment and learning 

with a fully integrated, interactive eBook. The new eBooks can be 

integrated with select ALEKS course products, and are high quality, 

interactive versions of their physical counterparts. They offer robust 

virtual features, including highlighting, bookmarking, and notetaking, 

and allow students and instructors to access the full textbook content, 

as well as multimedia resources (i.e. videos, images, exercises, etc.). 

Connect Math Hosted by ALEKS Corp., McGraw-Hill’s new 

online homework platform provides accurate content developed by 

the authors and subject matter experts, with the ALEKS Corporation 

providing their expertise in ensuring the content is accurate. 

Side-by-Side Graphical and Algebraic Examples – These examples 

enhance students understanding of the relationship between 

the two approaches by showing that there is more than one way to 

solve problems. 

Applications – Highly relevant and true-to-life application exercises 

are hallmark to any Coburn/Herdlick series. The authors have 

focused on creating applications of the highest quality, born from their 

life experiences and everyday occurrences. Finally, because of the 

emphasis and focus on applications, the authors have accomplished 

the feat of providing a large quantity of applications that span across 

many fields of study. 

Now Try Boxes – Located after each example, the “Now Try” 

boxes guide students to specific matched exercises at the end of 

each section. 

Mid-Chapter Checks – Included in every chapter are mid-chapter 

check exercise sets that asses students understanding of the material 

presented through the first half of the chapter. 

Student-Friendly Exposition – The authors have focused on 

writing a text that “speaks to students”, relating concepts in a form 

and at a level they understand and can relate to. This engaging writing 

style is designed to provide students with a positive experience 

that encourages students to read the text and not just use it for the 

exercise sets and examples. 

Chapter Connections – Chapter openers titled Chapter Connections 

are located at the beginning of each chapter and highlight an 

interesting application exercise from the chapter. They also provide a 

list of other real world connections to give students further representation 

of how the material in the chapter relates to their lives. 

Design Elements – McGraw-Hill partnered with students to learn 

how they use the text and as a result, we were able to incorporate 

design features that help students who learn in a variety of ways. 

Features that were based on student feedback include learning 

objectives and check points, caution boxes and boxed examples 

which are called out in the margin. Exercise sets were updated with 

bolded directions and backgrounds that are set in an off-white color 

to avoid glaring. 

Extending the Concept Exercises – Located in the end of section 

exercise sets, these problems require students to synthesize related 

concepts and use higher-order thinking skills. 

Maintaining Your Skills Exercises – Address skills from previous 

sections to encourage retention of previously learned information. 

Cumulative Review Exercise Sets – Included at the end of every 

chapter (starting with Chapter 2), these exercise incorporate material 

from all previous chapters to encourage retention of previously learned 

skills and concepts. These exercise sets emphasize the connections 

between the content presented from chapter to chapter. 

Concepts and Vocabulary and Working with Formulas Exercises 

– The end-of-section exercise sets include concepts and vocabulary 

problems that have been designed to help students review and understand 

important definitions and ideas and working with formulas 

exercises that are designed to enhance students’ comfort level when 

working with literals instead of numbers. 

Calculator Exploration and Discovery Sections – Found in every 

chapter, these sections provide instructors with long form problems 

that are designed to explore the full potential of a graphing calcula- 

57

Precalculus 

tor and provide the opportunity to investigate patterns and discover 

connections that might be overlooked. 

Making Connections Matching Problems – Each chapter contains 

a group of problems where students must identify graphs based on an 

equation or description. This requires students to make connections 

graphically, symbolically, numerically and verbally. 

Homework Selection Guide – Each section contains a homework 

selection guide with Core, Standard, Extended, and In Depth assignment 

suggestions to help instructors determine which problems they 

could assign to achieve a desired outcome. 

CONTENTS 

Chapter R: A Review of Basic Concepts and Skills 

R.1: Algebraic Expressions and the Properties of Real Numbers 

R.2: Exponents, Scientific Notation, and a Review of Polynomials 

R.3: Factoring Polynomials and Solving Polynomial Equations by 

Factoring 

R.4: Rational Expressions and Equations 

R.5: Radicals, Rational Exponents, and Radical Equations 

Chapter 1: Functions and Graphs 

1.1: Rectangular Coordinates, Graphing Circles and Other Relations 

1.2: Functions, Function Notation, and the Graph of a Function 

1.3: Linear Equations and Rates of Change 

1.4: Linear Functions, Special Forms, and More on Rates of Change 

1.5: Solving Equations and Inequalities Graphically; Formulas and 

Problem Solving 

1.6: Linear Models and Real Data 

Chapter 2: Relations, More on Functions 

2.1: Analyzing the Graph of a Function 

2.2: The Toolbox Functions and Transformations 

2.3: Absolute Value Functions, Equations, and Inequalities 

2.4: Rational and Radical Functions; More on the Domain 

2.5: Piecewise-Defined Functions 

2.6: Variation: The Toolbox Functions in Action 

Chapter 3: Quadratic Functions and Operations on Functions 

3.1: Complex Numbers 

3.2: Solving Quadratic Equations and Inequalities 

3.3: Quadratic Functions and Applications 

3.4: Quadratic Models; More on Rates of Change 

3.5: The Algebra of Functions 

3.6: Composition of Functions and the Difference Quotient 

Chapter 4: Polynomial and Rational Functions 

4.1: Synthetic Division; the Remainder and Factor Theorems 

4.2: The Zeros of Polynomial Functions 

4.3: Graphing Polynomial Functions 

4.4: Graphing Rational Functions 

4.5: Additional Insights into Rational Functions 

4.5: Additional Insights into Rational Functions 


5.1: One-to-One and Inverse Functions 

5.2: Exponential Functions 

5.3: Logarithms and Logarithmic Functions 

5.4: Properties of Logarithms 

5.5: Solving Exponential/Logarithmic Equations 

5.6: Applications from Business, Finance, and Science 

5.7: Exponential, Logarithmic, and Logistic Equation Models 

Chapter 6: Systems of Equations and Inequalities 

6.1: Linear Systems in Two Variables with Applications 

6.2: Linear Systems in Three Variables with Applications 

6.3: Nonlinear Systems of Equations and Inequalities 

6.4: Systems of Inequalities and Linear Programming 

Chapter 7: Matrices and Matrix Applications 

7.1: Solving Linear Systems Using Matrices and Row Operations 

7.2: The Algebra of Matrices 

7.3: Solving Linear Systems Using Matrix Equations 

7.4: Applications of Matrices and Determinants: Cramer’s rule, Partial 

Fractions, and More 

Chapter 8: Analytic Geometry and the Conic Sections 

8.1: A Brief Introduction to Analytic Geometry 

8.2: The Circle and the Ellipse 

8.3: The Hyperbola 

8.4: The Analytic Parabola 


9.1: Sequences and Series 

9.2: Arithmetic Sequences 

9.3: Geometric Sequences 

9.4: Mathematical Induction 

9.5: Counting Techniques 

9.6: Introduction to Probability 

9.7: The Binomial Theorem 

Appendices 

The Language, Notation, and Numbers of Mathematics 

Geometry Review with Unit Conversions 

More on Synthetic Division 

More on Matrices 

Deriving the Equation of a Conic 

Proof Positive--A Selection of Proofs from College Algebra 

NEW *9780077350161* 


9th Edition 

By Raymond Barnett, Merritt College, Michael 

Ziegler, Marquette University, and Karl Byleen, 

Marquette University 


ISBN: 9780077350161 

www.mhhe.com/barnett 

The Barnett/Ziegler/Byleen/Sobecki College Algebra series is designed 

to give students a solid grounding in pre-calculus topics in a 

user-friendly manner. The series emphasizes computational skills, 

ideas, and problem solving rather than theory. Explore/Discuss boxes 

integrated throughout each text encourage students to think critically 

about mathematical concepts. All worked examples are followed by 

Matched Problems that reinforce the concepts being taught. New 

to these editions, Technology Connections illustrate how concepts 

that were previously explained in an algebraic context may also 

be solved using a graphing calculator. Students are always shown 

 

calculator-dependent. In addition, each text in the series contains an 

abundance of exercises - including numerous calculator-based and 

reasoning and writing exercises - and a wide variety of real-world 

applications illustrating how math is useful. 


Technology Connections illustrate how concepts that were previously 

explained in an algebraic context may also be solved using a 

graphing calculator. Students are always shown the underlying algebraic 

methods first so that they do not become calculator-dependent. 

In addition, each text in the series contains an abundance of exercises 

- including numerous calculator-based and reasoning and writing 

exercises - and a wide variety of real-world applications illustrating 

how math is useful. 

CONTENTS 

CHAPTER R: BASIC ALGEBRAIC OPERATIONS 

R-1 Algebra and Real Numbers 

R-2 Exponents 

R-3 Radicals 

R-4 Polynomials: Basic Operations 

Chapter R Review 

58

Precalculus 

CHAPTER 1: EQUATIONS AND INEQUALITIES 

1-1 Linear Equations and Applications 


1-3 Absolute Value 

1-4 Complex Numbers 

1-5 Quadratic Equations and Applications 

1-6 Equations Involving Radicals 

Chapter 1 Group Activity: Solving a Cubic Equation 


CHAPTER 2: GRAPHS 

2-1 Cartesian Coordinate System 

2-2 Distance in the Plane 

2-3 Equations of a Line 

2-4 Linear Equations and Models 

Chapter 2 Group Activity: Rates of Change 


CHAPTER 3: FUNCTIONS 

3-1 Functions 

3-2 Graphing Functions 

3-3 Transformations of Functions 

3-4 Quadratic Functions 

3-5 Combining Functions; Composition 

3-6 Inverse Functions 

Chapter 3 Group Activity: Mathematical Modeling - Choosing a Long- 

Distance Calling Plan 


1, 2, & 3 Cumulative Review Exercises 

CHAPTER 4: POLYNOMIAL AND RATIONAL FUNCTIONS 

4-1 Polynomial Functions And Models 

4-2 Real Zeros and Polynomial Inequalities 

4-3 Complex Zeros and Rational Zeros of Polynomials 

4-4 Rational Functions and Inequalities 

4-5 Variation and Modeling 

Chapter 4 Group Activity: Interpolating Polynomials 


CHAPTER 5: EXPONENTIAL AND LOGARITHMIC FUNCTIONS 

5-1 Exponential Functions 

5-2 Exponential Models 

5-3 Logarithmic Functions 

5-4 Logarithmic Models 

5-5 Exponential and Logarithmic Equations 

Chapter 5 Group Activity: Growth of Increasing Functions 


4 & 5 Cumulative Review Exercises 

CHAPTER 6: ADDITIONAL TOPICS IN ANALYTIC GEOMETRY 

6-1 Conic Sections; Parabola 

6-2 Ellipse 

6-3 Hyperbola 

Chapter 6 Group Activity: Focal Chords 


CHAPTER 7: SYSTEMS OF EQUATIONS AND INEQUALITIES; 

MATRICES 


7-2 Solving Linear Systems Using Gauss-Jordan Elimination 

7-3 Matrix Operations 

7-4 Solving Linear Systems Using Inverse Matrices 

7-4 Determinants and Cramer’s Rule 

7-5 Chapter 7 Group Activity: Modeling with Systems of Linear 

Equations 

7-6 Systems of Nonlinear Equations 

7-7 Systems of Linear Inequalities 



CHAPTER 8: SEQUENCES AND SERIES 

8-1 Sequences and Series 

8-2 Mathematical Induction 


8-4 Counting Techniques: Multiplication Principle, Permutations, and 

Combinations 

8-5 Sample Spaces and Probability 

8-6 Binomial Formula 

Chapter 8 Group Activity: Sequences Specified by Recursion Formulas 



APPENDIX A: SPECIAL TOPICS 

A-1 Scientific Notation and Significant Digits 

A-2 Partial Fractions 

A-3 Parametric Equations 

APPENDIX B 

B-1 Geometric Formulas 


2nd Edition 

By John W. Coburn, Saint Louis Community College-Florissant Valley 


ISBN: 9780077276492 

ISBN: 9780071220033 [IE] 


Three components contribute to a theme sustained throughout 

 

framework, and providing strong connections. Not only does Coburn 

present a sound problem-solving process to teach students to recognize 

a problem, organize a procedure, and formulate a solution, 

the text encourages students to see beyond procedures in an effort 

to gain a greater understanding of the big ideas behind mathematical 

concepts. Written in a readable, yet mathematically mature manner 

appropriate for college algebra level students, Coburn’s College Algebra 

uses narrative, extensive examples, and a range of exercises 

to connect seemingly disparate mathematical topics into a cohesive 

whole. Coburn’s hallmark applications are born out of the author’s 

extensive experiences in and outside the classroom, and appeal to 

the vast diversity of students and teaching methods in this course 

 

students across the country, College Algebra second edition, continues 

to emphasize connections in order to improve the level of student 

engagement in mathematics and increase their chances of success 

in college algebra. 

CONTENTS 


R-1 The Language, Notation, and Numbers of Mathematics 

R-2 Algebraic Expressions and the Properties of Real Numbers 

R-3 Exponents, Scientific Notation, and a Review of Polynomials 

R-4 Factoring Polynomials 

R-5 Rational Expressions 

R-6 Radicals and Rational Exponents 

Chapter 1: Equations and Inequalities 

1-1 Linear Equations, Formulas, and Problem Solving 

1-2 Linear Inequalities in One Variable 

1-3 Absolute Value Equations and Inequalities 



1-6 Solving Other Types of Equation 

Chapter 2: Relations, Functions and Graphs 

2-1 Rectangular Coordinates; Graphing Circles and Relations 

2-2 Graphs of Linear Equations 

2-3 Linear Equations and Rates of Change 

2-4 Functions, Notation, and Graphs of Functions 

2-5 Analyzing the Graph of a Function 

2-6 Toolbox Functions and Transformations 

2-7 Piecewise-Defined Functions 

2-8 The Algebra and Composition of Functions 


3-1 Quadratic Functions and Applications 

3-2 Synthetic Division; The Remainder and Factor Theorems 

3-3 The Zeroes of Polynomial Functions 

3-4 Graphing Polynomial Functions 

3-5 Graphing Rational Functions 

59

Precalculus 

3-6 Additional Insights into Rational Functions 

3-7 Polynomial and Rational Inequalities 

3-8 Variation: Function Models in Action 


4-1 One-to-One and Inverse Functions 


4-3 Logarithms and Logarithmic Functions 

4-4 Properties of Logarithms; Solving Exponential and Logarithmic 

Equations 

4-5 Applications from Business, Finance, and Science 

4-6 Business, Finance, and Science Applications 


5-1 Linear Systems in Two Variables with Applications 

5-2 Linear Systems in Three Variables with Applications 

5-3 Nonlinear Systems of Equations and Inequalities 

5-4 Systems of Inequalities and Linear Programming 


6-1 Solving Systems Using Matrices and Row Operations 

6-2 The Algebra of Matrices 

6-3 Solving Linear Systems Using Matrix Equations 

6-4 Applications of Matrices and Determinants: 

Chapter 7: Analytical Geometry and Conic Sections 

7-1 Introduction to Analytic Geometry 

7-2 The Circle and the Ellipse 

7-3 The Hyperbola 

7-4 The Analytic Parabola 



8-2 Arithmetic Sequences 

8-3 Geometric Sequences 


8-5 Counting Techniques 

8-6 Introduction to Probability 

8-7 The Binomial Theorem 

APPENDICES 

A-1 More on Synthetic Division 

A-2 More on Matrices 

A-3 Deriving the Equation of a Conic 

A-4 Proof Positive--A Selection of Proofs from College Algebra 

COLLEGE ALGEBRA ESSENTIALS 

2nd Edition 

John W. Coburn, Saint Louis Community College-Florissant Valley 


ISBN: 9780077297909 



 



a problem, organize a procedure, and formulate a solution, the 

text encourages students to see beyond procedures in an effort to 

gain a greater understanding of the big ideas behind mathematical 


appropriate for college algebra level students, Coburn’s College 

Algebra Essentials uses narrative, extensive examples, and a range 

of exercises to connect seemingly disparate mathematical topics into 

a cohesive whole. Coburn’s hallmark applications are born out of the 

author’s extensive experiences in and outside the classroom, and 

appeal to the vast diversity of students and teaching methods in this 

 

and students across the country, College Algebra Essentials second 

edition, continues to emphasize connections in order to improve 

the level of student engagement in mathematics and increase their 

chances of success in college algebra. 

CONTENTS 














1-6 Solving Other Types of Equations 
























Equations 








APPENDICES 




A-4 Proof Positive--A Selection of Proofs from from College Algebra 

60

Precalculus 

COLLEGE ALGEBRA: GRAPHS AND 

MODELS 

3rd Edition 

By Raymond A Barnett, Merritt College, Michael R Ziegler and Karl 

E Byleen of Marquette University, David Sobecki, Miami University- 

Hamilton 


ISBN: 9780077221287 (Mandatory Package) 


The Barnett Graphs & Models series in college algebra and 

precalculus maximizes student comprehension by emphasizing 

computational skills, real-world data analysis and modeling, and 

problem solving rather than mathematical theory. Many examples 

feature side-by-side algebraic and graphical solutions, and each is 

followed by a matched problem for the student to work. This active 

involvement in the learning process helps students develop a more 

thorough understanding of concepts and processes. A hallmark of 

the Barnett series, the function concept serves as a unifying theme. 

A major objective of this book is to develop a library of elementary 

functions, including their important properties and uses. Employing 

this library as a basic working tool, students will be able to proceed 

 

 

to analyze the graph and use it to solve the problem. Applications 

included throughout the text give the student substantial experience 

in solving and modeling real world problems in an effort to convince 

even the most skeptical student that mathematics is really useful. 

CONTENTS 

CHAPTER 1 FUNCTIONS, GRAPHS, AND MODELS 

1-1 Using Graphing Utilities 

1-2 Functions 

1-3 Functions: Graphs and Properties 

1-4 Functions: Graphs and Transformations 

1-5 Operations on Functions; Composition 



Chapter 1 Group Activity: Mathematical Modeling–Choosing a Long 


CHAPTER 2 MODELING WITH LINEAR AND QUADRATIC FUNC- 

TIONS 

2-1 Linear Functions 




2-5 Quadratic Equations and Models 

2-6 Additional Equation Solving Techniques 

2-7 Solving Inequalities 


Chapter 2 Group Activity: Mathematical Modeling in Population 

Studies 

Cumulative Review Exercise for Chapters 1 and 2 

CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS 


3-2 Polynomial Division 







CHAPTER 4 MODELING WITH EXPONENTIAL AND LOGARITHMIC 

FUNCTIONS 







Cumulative Review Chapters 3 and 4 

Chapter 4 Group Activity: Comparing Regression Models 


CHAPTER 5 MODELING WITH SYSTEMS OF EQUATIONS AND 

INEQUALITIES 

5-1 Systems of Linear Equations in Two Variables 

5-2 Systems of Linear Equations in Three Variables 




Chapter 5 Group Activity: Modeling with Systems of Equations 

CHAPTER 6 MATRICES AND DETERMINANTS 

6-1 Matrix Solutions to Linear Systems 


6-3 Inverse of a Square Matrix 

6-4 Matrix Equations and Systems of Linear Equations 

6-5 Determinants 

6-6 Properties of Determinants 



Chapter 6 Group Activity: Using Matrices to Find Cost, Revenue, 

and Profit 


CHAPTER 7 SEQUENCES, INDUCTION, PROBABILITY 




7-4 Multiplication Principle, Permutations, and Combinations 




Chapter 7 Group Activity: Sequences Specified by Recursion Formulas 

CHAPTER 8 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY 


8-2 Ellipse 

8-3 Hyperbola 


8-5 Rotation of Axes 




Appendix A BASIC ALGEBRA REVIEW 

A-1 Algebra and Real Numbers 

A-2 Exponents 

A-3 Radicals 

A-4 Polynomials: Basic Operations 

A-5 Polynomials: Factoring 

A-6 Rational Expressions: Basic Operations 

A-7 Linear Equations and Inequalities 

A-8 Cartesian Coordinate System 

A-9 Basic Formulas in Analytic Geometry 

Appendix A Review 

Appendix A Group Activity: Rational Number Representations 

Appendix B SPECIAL TOPICS 

B-1 Significant Digits 

B-2 Partial Fractions 

B-3 Parametric Equations 

Appendix C GEOMETRIC FORMULAS 

61

Precalculus 

SCHAUM’S EASY OUTLINE OF COLLEGE 

ALGEBRA 

2nd Edition 

By Robert Moyer, Fort Valley State College and Murray R Spiegel (deceased) 


ISBN: 9780071745840 


If you are looking for a quick nuts-and-bolts overview of college algebra, 

it’s got to be Schaum’s Easy Outline. This book is a pared-down, 

 

with an emphasis on clarity and conciseness. 






fields 


Topics include: Fundamental Tools of Algebra, Algebraic Expressions 

and Operations, Functions, Quadratic Equations, Sequences, Series, 

and Mathematical Induction, Permutations, Combinations, the Binomial 

Therorem, and Probability 

CONTENTS 

1. Fundamental Tools of Algebra; 

2. Algebraic Expressions and Operations; 

3. Functions; 

4. Quadratic Equations; 

5. Sequences, Series, and Mathematical Induction; 

6. Permutations, Combinations, the Binomial Therorem, and Probability; 

Index 


COLLEGE ALGEBRA DEMYSTIFIED 

By Rhonda Huettenmueller, University of North Texas 

2004 / 446 pages 

ISBN: 9780071439282 


CONTENTS 

Preface 

Chapter 1: Completing the Square 

Chapter 2: Absolute Value Equations and Inequalities 

Chapter 3: The xy Coordinate Plane 

Chapter 4: Lines and Parabolas 

Chapter 5: Nonlinear Inequalities 

Chapter 6: Functions 

Chapter 7: Quadratic Functions 

Chapter 8: Transformations and Combinations 

Chapter 9: Polynomial Functions 


Chapter 11: Exponents and Logarithms 

Appendix (Final Exam and Index) 

Trigonometry 

SCHAUM’S OUTLINE OF COLLEGE 

ALGEBRA 

3rd Edition 

By Robert Moyer, Ph.D., Fort Valley State College, and Murray R. 

Spiegel, Deceased 

2010 (August 2009) / 376 pages / Softcover 

ISBN: 9780071635394 


Algebra, the foundation for all higher mathematics, is explained to 

both beginners and those reviewing algebra for further work in math, 

 

tion that sold more than 600,000 copies--examines the most current 

terminology, emphasis, and technology. The new edition also includes: 

 

 

 

Greater emphasis on graphing calculators 

Clarified material on logarithms and determinants 

A simplified review of fractions 

NEW 

*9780077349974* 

TRIGONOMETRY 

2nd Edition 

By John Coburn, St Louis Community College- 

Flors Valley 


ISBN: 9780077349974 



 







appropriate for college algebra level students, Coburn’s Trigonometry 

uses narrative, extensive examples, and a range of exercises 

to connect seemingly disparate mathematical topics into a cohesive 




 

students across the country, Trigonometry, Second Edition, continues 




62

Precalculus 


Exercises - a wealth of exercises support the text’s main ideas, 

and due to their raneg of difficulty, there is strong support for weaker 

students, while advanced studetns are challenged to reach even 

further. 

Examples - abundant examples carefully prepare the students 

for homework and exams. Easily located on the page, Coburn’s 

numerous examples expose the learner to more exercise types than 

most other texts. 

Applications - large quantity of applications that explore a wide 

variety of interests and illustrate how mathematics is connected to 

other disciplinens and the world around us. 

Student-friendly exposition - Coburn provides a smooth and 

conversational writing style that includes helpful hints, mathematical 

connections, cautions and opportunities for further exploration. 

MATHZONE - MathZone sets the bar for classroom technology. 

Algorithmically generated problems, video lectures, interactice 

exercise walk-throughs, as well as, online testing and assessment 

using ALEKS technology, which all feed to a unified gradebook. www. 

mathzone.com 

ALEKS (Assessment and LEarning in Knowledge Spaces) - an 

artificial intelligence-based system for mathematics and statistics 

learning, available online 24/7. Using unique adaptive questioning, 

ALEKS accurately assesses what topics each students knows and 

then determines exactly what each student is ready to learn next. 

ALEKS interacts with a student much as a skilled human tutor would, 

moving between explanation and practice as needed, correcting and 

analyzing errors, defining terms and changing topics on request, and 

helping them master the course content more quickly and easily. 

www.highed.aleks.com. 

CONTENTS 

Chapter 1: Introduction to Trigonometry 

1.1 Angle Measure and Special Triangles 

1.2 Properties of Triangles; Similar Triangles 

Mid-Chapter Check 

RBC: More on Special Triangles 

1.3 Trigonometry: A View from the Coordinate Plane 

1.4 Fundamental Identities and Families of Identities 

Summary/Concept Rev, Mixed Rev, Practice Test 

Calc Exploration and Discovery: The Range of Sine, Cosine, and 

Tangent 

SCS: Creating New Identities 

Chapter 2: Right Triangles & Static Trigonometry 

2.1 A Right Triangle View of Trigonometry 

2.2 Solving Right Triangles 


RBC: The Area of a Triangle 

2.3 Applications of Static Trigonometry 

2.4 Extending Beyond Acute Angles 


Calc Exploration and Discovery: Solving Triangles 

SCS: Standard Angles, Reference Angles, and the Trig Functions 

Cumulative Review 1 - 2 

Chapter 3: Radian Measure & Dynamic Trigonometry 

3.1 Angle Measure in Radians 

3.2 Arc Lengths, Velocities, and the Area of a Circular Sector 


RBC: More on Radians 

3.3 The Unit Circle 

3.4 The Trigonometry of Real Numbers 


Calc Exploration and Discovery: Signs, Quadrants and Reference Arcs 

SCS: Trigonometry of the Real Numbers and the Wrapping Function 


Chapter 4: Trigonometric Graphs and Models 

4.1 Graphs of Sine and Cosine Functions 

4.2 Graphs of Cosecant, Secant, Tangent and Cotangent Functions 


RBC: Trigonometric Potpourri 

4.3 Transformations of Trigonometric Graphs 

4.4 Trigonometric Applications and Models 


Calc Exploration and Discovery 

SCS 

Cumulative Review 1 – 4 

Modeling With Technology: Trigonometric Equation Models 

Chapter 5: Trigonometric Identities 

5.1 More on Verifying Identities 

5.2 The Sum and Difference Identities 

Mid-Chapter Check RBC: Understanding Identities 

5.3 The Double Angle and Half Angle Identities 

5.4 The Product-to-Sum and Sum-to-Product Identities 



SCS 


Chapter 6: Inverse Functions and Trigonometric Equations 

6.1 One-to-One and Inverse Functions 

6.2 Inverse Trigonometric Functions and their Applications 

Mid -Chapter Check 

RBC: More on Equation Solving 

6.3 Solving Basic Trigonometric Equations 

6.4 General Trigonometric Equations and Applications 



SCS: Trigonometric Equations and Inequalities 


Chapter 7: Applications of Trigonometry 

7.1 Oblique Triangles and the Law of Sines 

7.2 The Law of Cosines; the Area of a Triangle 

Mid -Chapter Check 

RBC 

7.3 Vectors and Vector Diagrams 

7.4 Vectors Applications and the Dot Product 



SCS 


Chapter 8: Trigonometric Connections to Algebra 


8.2 Complex Numbers in Trigonometric Form 

8.3 Demoivre’s Theorem and the nth Roots Theorem 


RBC 

8.4 Polar Coordinates and Equations 

8.5 Graphs of Polar Equations 

8.6 Parametric Equations and Graphs 



SCS 

Cumulative Review 1 – 8 

Appendices 

A.1 Exponential and Logarithmic Functions 

A.2 Review and Technology 

 

 

 

 

 

63

Precalculus 

SCHAUM’S OUTLINE OF TRIGONOMETRY 

4th Edition 

By Robert Moyer, Fort Valley State University and Frank Ayres (deceased) 

2009 (July 2008) / 211 pages 

ISBN: 9780071543507 




thousands of college and high school students who enroll in trigonometry 

courses. 

CONTENTS 

1. Angles and Applications 

2. Trigonometric Functions of a General Angle 

3. Trigonometric Functions of an Acute Angle 

4. Solutions of Right Triangles 

5. Practical Applications 

6. Reduction to Functions of Positive Acute Angles 

7. Variation and Graphs of the Trigonometric Functions 

8. Basic Relationships and Identities 

9. Trigonometric Functions of Two Angles 

10. Sum, Difference, and Product Formulas 

11. Oblique Triangles 

12. Area of a Triangle 

13. Inverses of Trigonometric Functions 

14. Trigonomeric Equations 

15. Complex Numbers 


Chapter 6. Three-Space and Vectors 


PART TWO: HOW IS TRIGONOMETRY USED? 

Chapter 7. Scientific Notation 

Chapter 8. Surveying, Navigation, and Astronomy 

Chapter 9. Waves and Phase 

Chapter 10. Reflection and Refraction 

Chapter 11. Global Trigonometry 


FINAL EXAM 

ANSWERS TO QUIZ, TEST, AND EXAM QUESTIONS 


INDEX 

College Algebra with 

Trigonometry 


NEW *9780077350109* 

COLLEGE ALGEBRA WITH 

TRIGONOMETRY 

9th Edition 

By Raymond A Barnett, Merritt College, 

Michael Ziegler and Karl Byleen of Marquette 

University 

TEACH YOURSELF TRIGONOMETRY 

2nd Edition 

By P Abbott 

2003 / 176 pages 

ISBN: 9780071421355 


Teach Yourself Trigonometry is suitable for beginners, but it also goes 

beyond the basics to offer comprehensive coverage of more advanced 

topics. Each chapter features numerous worked examples and many 

carefully graded exercises, and full demonstrations of trigonometric 

proofs are given in the answer key. 

TRIGONOMETRY DEMYSTIFIED 


2003 / 303 pages 

ISBN: 9780071416313 


CONTENTS 

Preface 

Acknowledgments 

PART ONE: WHAT IS TRIGONOMETRY? 

Chapter 1. The Circle Model 

Chapter 2. A Flurry of Facts 

Chapter 3. Graphs and Inverses 

Chapter 4. Hyperbolic Functions 

Chapter 5. Polar Coordinates 

2011 (January 2010) / 896 pages 

ISBN: 9780077350109 

ISBN: 9780071221757 [IE] 

ISBN: 9780077941840 (with MathZone Access Card) 


Barnett, Ziegler, Byleen, and Sobecki’s College Algebra with Trigonometry 

text is designed to be user friendly and to maximize student 

comprehension by emphasizing computational skills, ideas, and 

problem solving as opposed to mathematical theory. The large number 

of pedagogical devices employed in this text will guide a student 

through the course. Integrated throughout the text, students and 

 

to think critically about mathematical concepts. In each section, the 

worked examples are followed by matched problems that reinforce 

the concept being taught. In addition, the text contains an abundance 

of exercises and applications that will convince students that math is 

useful. A MathZone site featuring algorithmic exercises, videos, and 

other resources accompanies the text. 

FEATURES 

Appealing Visuals: The design has been completely updated 

in full color and now offers a more contemporary and inviting visual 

backdrop for the concepts. Photos have been added to enhance the 

text and contribute to the updated appearance. 

Examples and Matched Problems: Detailed worked examples 

-- now with expanded color notes for students that outline the solution 

steps in words -- appear frequently throughout the sections to introduce 

concepts and demonstrate problem-solving techniques. Each 

example is followed by a Matched Problem to help students solidify 

64

Precalculus 

their understanding and play an active role in the learning process. 

For easy reference, answers to the Matched Problems appear at the 

end of each section. 

Technological Support: New “Technology Connections” boxes 

integrated at appropriate points in the text illustrate how techniques 

previously introduced in an algebraic context may be solved using 

a graphing calculator. Students always learn the algebraic methods 

first so that they develop a solid grasp of these methods and do not 

become calculator-dependent. The exercise sets contain calculatorbased 

exercises that are clearly marked with a calculator icon. The 

use of technology is completely optional with this text. All technology 

features and exercises may be omitted without sacrificing content 

coverage. 

Exploration and Discussion: Integrated at appropriate places 

in each section, Explore/Discuss boxes encourage students to think 

critically about mathematics. These features also provide excellent 

opportunities for group work. 

Balanced Exercise Sets: The exercise sets at the end of each 

section and chapter contain a mix of skill exercises, calculator exercises, 

reasoning and writing exercises, and applied exercises. The 

exercises are graded by difficulty level, becoming progressively harder 

as students gain confidence in their skills. However, the old A/B/C 

subdivisions have been omitted so that students will not be daunted 

by seeing problems labeled as being more difficult. These subdivisions 

may be found in the Instructor’s Solutions Manual. 

Opportunities for Reviewing and Expanding Knowledge: Chapter 

Review sections at the end of each chapter provide a thorough 

review of the important terms and topics in the chapter. Following 

this recap is a comprehensive set of Chapter Review Exercises. 

Cumulative Review Exercises appear every two or three chapters 

for additional reinforcement. Every chapter contains a Group Activity 

that allows students to work with classmates to explore chapter 

topics in greater detail. 

Objective-Based Learning: Introductory section objectives help 

provide a road map through the topics of the section. The Chapter 

Reviews are organized by section objective. 

Right Triangle Approach: College Algebra with Trigonometry 

takes a right angle approach to the initial coverage of trigonometry. 

CONTENTS 



R-2 Exponents and Radicals 

R-3 Polynomials: Basic Operations and Factoring 

R-4 Rational Expressions: Basic Operations 












2-1 Rectangular Coordinates 







3-1 Functions 



























CHAPTER 6: TRIGONOMETRIC FUNCTIONS 

6-1 Angles and Their Measure 

6-2 Right Triangle Trigonometry 

6-3 Trigonometric Functions: A Unit Circle Approach 

6-4 Trigonometric Functions: Properties and Graphs 

6-5 More General Trigonometric Functions 

6-6 Inverse Trigonometric Functions 

Chapter 6 Group Activity: A Predator-Prey Analysis Involving Mountain 

Lions and Deer 


CHAPTER 7: TRIGONOMETRIC IDENTITIES AND CONDITIONAL 

EQUATIONS 

7-1 Basic Identities and Their Use 

7-2 Sum, Difference, and Cofunction Identities 

7-3 Double-Angle and Half-Angle Identities 

7-4 Product-Sum and Sum-Product Identities 

7-5 Trigonometric Equations 

Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin(Bt + C) - A 

Harmonic Analysis Tool 


CHAPTER 8: ADDITIONAL TOPICS IN TRIGONOMETRY 

8-1 Law of Sines 

8-2 Law of Cosines 

8-3 Vectors in the Plane 

8-4 Polar Coordinates and Graphs 

8-5 Complex Numbers and De Moivre’s Theorem 

Chapter 8 Group Activity: Conic Sections and Planetary Orbits 





9-2 Ellipse 

9-3 Hyperbola 





MATRICES 






Chapter 10 Group Activity: Modeling with Systems of Linear Equations 






65

Precalculus 




11-4 Counting Techniques: Multiplication Principle, Permutations, 

and Combinations 



Chapter 11 Group Activity: Sequences Specified by Recursion 

Formulas 


9. 10, & 11 Cumulative Review Exercises 

CHAPTER 12: LIMITS: AN INTRODUCTION TO CALCULUS 

12-1 Introduction to Limits 

12-2 Computing Limits Algebraically 

12-3 Limits at Infinity 

12-4 The Derivative 

12-5 Area and Calculus 

Chapter 12 Group Activity: Derivatives of Exponential and Log Functions 






APPENDIX B 



ALGEBRA & TRIGONOMETRY 

2nd Edition 

By John W. Coburn, Saint Louis Community College-Florissant Valley 

2010 (February 2009) / Hardcover / 1200 pages 

ISBN: 9780077276515 

ISBN: 9780070173002 [IE] 



 







appropriate for college algebra level students, Coburn’s Algebra & 

Trigonometry uses narrative, extensive examples, and a range of 

exercises to connect seemingly disparate mathematical topics into a 

cohesive whole. Coburn’s hallmark applications are born out of the 

author’s extensive experiences in and outside the classroom, and 

appeal to the vast diversity of students and teaching methods in this 

 

and students across the country, Algebra & Trigonometry second edition, 

continues to emphasize connections in order to improve the level 

of student engagement in mathematics and increase their chances 

of success in college algebra. 

CONTENTS 






































Equations 



Chapter 5: Introduction to Trigonometric Functions 

5-1 Angle Measure, Special Triangles, and Special Angles 

5-2 The Trigonometry of Right Triangles 

5-3 Trigonometry and the Coordinate Plane 

5-4 Unit Circles and the Trigonometric of Real Numbers 

5-5 Graphs of Sine and Cosine Functions; Cosecant and Secant 

Functions 

5-6 Graphs of Tangent and Cotangent Functions 

5-7 Transformations and Applications of Trigonometric Graphs 

Chapter 6: Trigonometric Identities, Inverses, and Equations 

6-1 Fundamental Identities and Families of Identities 

6-2 Constructing and Verifying Identities 

6-3 The Sum and Difference Identities 

6-4 Double Angle, Half Angle & Product-to-Sum Identities 

6-5 The Inverse Trigonometric Functions and Their Applications 

6-6 Solving Basic Trigonometric Equations 

6-7 General Trigonometric Equations and Applications 


7-1 Oblique Triangles and the Law of Sines 

7-2 The Law of Cosines; Area of a Triangle 

7-3 Vectors and Vector Diagrams 

7-4 Vector Applications and the Dot Product 

7-5 Complex Numbers in Trigonometric Form 

7-6 Demoivre’s Theorem and the Theorem on nth Roots 










9-4 Applications of Matrices and Determinants: Cramer’s Rule, Partial 

Fractions, and More 

Chapter 10: Analytical Geometry and Conic Sections 





10-5 Polar Coordinates, Equations, and Graphs 

10-6 More on Conic Sections: Rotation of Axes and Polar Form 

10-7 Parametric Equations and Graphs 

66

Precalculus 








11-7 The Binomial Theorem Summary and Concept Review 

APPENDICES 




A-4 Proof Positive--A Selection of Proofs from Algebra and Trigonometry 

Precalculus 

NEW 

*9780073519531* 

PRECALCULUS 

Graphs & Models 

By John Coburn, Saint Louis CC-Flors Valley 

and JD (John) Herdlick, Saint Louis CC-Meramec-Kirkwood 


ISBN: 9780073519531 

Three components contribute to a theme sustained throughout the 

 

foundation, building a solid framework, and providing strong connections. 

In the Graphs and Models texts, the authors combine their 

depth of experience with the conversational style and the wealth of 

applications that the Coburn/Herdlick texts have become known for. 

By combining a graphical approach to problem solving with algebraic 

methods, students learn how to relate their mathematical knowledge 

to the outside world. The authors use technology to solve the more 

true to life equations, to engage more applications, and to explore the 

 

from the feedback of hundreds of instructors and students across the 

country, Precalculus: Graphs & Models emphasizes connections in 

order to improve the level of student engagement in mathematics and 

increase their chances of success in precalculus and calculus. The 

launch of the Coburn/Herdlick Graphs and Models series provides a 

 

McGraw-Hill’s new homework platform, Connect Math Hosted by 

ALEKS Corp. Math instructors served as digital contributors to choose 

the problems that will be available, authoring each algorithm and providing 

stepped out solutions that go into great detail and are focused 

on areas where students commonly make mistakes. From there, the 

ALEKS Corporation reviewed each algorithm to ensure accuracy. A 

unifying theme throughout the entire process was the involvement of 

the authors. Through each step, they provided feedback and guidance 

to the digital contributors to ensure that the content being developed 

digitally closely matched the textbook. The result is an online homework 

platform that provides superior content and feedback, allowing 


FEATURES 

ALEKS (Assessment and LEarning in Knowledge Spaces) – 

ALEKS is a Web-based, artificially intelligent assessment and learning 

system. ALEKS uses adaptive questioning to quickly and accurately 

determine exactly what a student knows and doesn’t know in a course. 

ALEKS then instructs the student on the topics she is most ready to 

learn. As a student works through a course, ALEKS periodically reassesses 

the student to ensure that topics learned are also retained. 

ALEKS courses are very complete in their topic coverage and ALEKS 

avoids multiple-choice questions. A student who shows a high level of 

mastery of an ALEKS course will be successful in the actual course he 

or she is taking. ALEKS also provides the advantages of one-on-one 

instruction, 24/7, from virtually any Web-based computer for a fraction 

of the cost of a human tutor. ALEKS 360 offers a cost-effective total 

course solution by providing powerful ALEKS personalized assessment 

and learning with a fully integrated, interactive eBook. The new 

eBooks can be integrated with select ALEKS course products, and 

are high quality, interactive versions of their physical counterparts. 

They offer robust virtual features, including highlighting, bookmarking, 

and notetaking, and allow students and instructors to access the 

full textbook content, as well as multimedia resources (i.e. videos, 

images, exercises, etc.). 

Connect Math Hosted by ALEKS Corp. , McGraw-Hill’s new 

online homework platform provides accurate content developed by 

the authors and subject matter experts, with the ALEKS Corporation 

providing their expertise in ensuring the content is accurate. 

Side-by-Side Graphical and Algebraic Examples – These examples 

enhance students understanding of the relationship between 

the two approaches by showing that there is more than one way to 

solve problems. 

Feature Applications – Highly relevant and true-to-life application 

exercises are hallmark to any Coburn/Herdlick series. The authors 

have focused on creating applications of the highest quality, born from 

their life experiences and everyday occurrences. Finally, because of 

the emphasis and focus on applications, the authors have accomplished 

the feat of providing a large quantity of applications that span 

across many fields of study. 

Now Try Boxes – Located after each example, the “Now Try” 

boxes guide students to specific matched exercises at the end of 

each section. 

Mid-Chapter Checks – Included in every chapter are mid-chapter 

check exercise sets that asses students understanding of the material 

presented through the first half of the chapter. 

Chapter Connections – Chapter openers titled Chapter Connections 

are located at the beginning of each chapter and highlight an 

interesting application exercise from the chapter. They also provide a 

list of other real world connections to give students further representation 

of how the material in the chapter relates to their lives. 

Design Elements – McGraw-Hill partnered with students to learn 

how they use the text and as a result, we were able to incorporate 

design features that help students who learn in a variety of ways. Features 

that were based on student feedback include learning objectives 

and check points, caution boxes and boxed examples which are called 

out in the margin. Exercise sets were updated with bolded directions 

and backgrounds that are set in an off-white color to avoid glaring. 

Extending the Concept Exercises – Located in the end of section 

exercise sets, these problems require students to synthesize related 

concepts and use higher-order thinking skills. 

Maintaining Your Skills Exercises – Address skills from previous 

sections to encourage retention of previously learned information. 

Cumulative Review Exercise Sets – Included at the end of every 

chapter (starting with Chapter 2), these exercise incorporate material 

from all previous chapters to encourage retention of previously learned 

skills and concepts. These exercise sets emphasize the connections 

between the content presented from chapter to chapter. 

Student-Friendly Exposition – The authors have focused on 

writing a text that “speaks to students”, relating concepts in a form 

and at a level they understand and can relate to. This engaging writ- 

67

Precalculus 

ing style is designed to provide students with a positive experience 

that encourages students to read the text and not just use it for the 

exercise sets and examples. 

Concepts and Vocabulary and Working with Formulas Exercises 

– The end-of-section exercise sets include concepts and vocabulary 

problems that have been designed to help students review and understand 

important definitions and ideas and working with formulas 

exercises that are designed to enhance students’ comfort level when 

working with literals instead of numbers. 

Calculator Exploration and Discovery Sections – Found in every 

chapter, these sections provide instructors with long form problems 

that are designed to explore the full potential of a graphing calculator 

and provide the opportunity to investigate patterns and discover 

connections that might be overlooked. 

Connections Matching Problems – Each chapter contains a group 

of problems where students must identify graphs based on an equation 

or description. This requires students to make connections graphically, 

symbolically, numerically and verbally. Benefit: This feature reinforces 

students’ ability to read and interpret graphs. It helps students make 

the connection between graphical and algebraic information while it 

enhances students’ ability to read and interpret graphical data. 

Homework Selection Guide – Each section contains a homework 

selection guide with Core, Standard, Extended, and In Depth assignment 

suggestions to help instructors determine which problems they 

could assign to achieve a desired outcome. 

Connections to Calculus – Where relevant, the authors have created 

Connections to Calculus sections that illustrate how topics from 

the chapters will be utilized in calculus. These sections help to make 

connections between the material students are currently learning and 

why it is relevant to their future study of calculus. 

CONTENTS 

Chapter 1: Functions and Graphs 

1.1, Rectangular Coordinates; Graphing Circles and Other Relations 

1.2, Linear Equations and Rates of Change 

1.3, Functions, Function Notation, and the Graph of a Function 

1.4, Linear Functions, Special Forms, and More on Rates of Change 

1.5, Solving Equations and Inequalities Graphically; Formulas and 

Problem Solving 

1.6, Linear Function Models and Real Data 

Chapter 2: Relations, More on Functions 

2.1, Analyzing the Graph of a Function 

2.2, The Toolbox Functions and Transformations 

2.3, Absolute Value Functions, Equations, and Inequalities 

2.4, Rational and Radical Functions; More on the Domain 

2.5, Piecewise-Defined Functions 

2.6, Variation: The Toolbox Functions in Action 

Chapter 3: Quadratic Functions and Operations on Functions 

3.1, Complex Numbers 

3.2, Solving Quadratic Equations and Inequalities 

3.3, Quadratic Functions and Applications 

3.4, Quadratic Models; More on Rates of Change 

3.5, The Algebra of Functions 

3.6, Composition of Functions and the Difference Quotient 


4.1, Synthetic Division; the Remainder and Factor Theorems 

4.2, The Zeros of Polynomial Functions 

4.3, Graphing Polynomial Functions 

4.4, Graphing Rational Functions 

4.5, Additional Insights into Rational Functions 

4.6, Polynomial and Rational Inequalities 


5.1, One-to-One and Inverse Functions 

5.2, Exponential Functions 

5.3, Logarithms and Logarithmic Functions 

5.4, Properties of Logarithms 

5.5, Solving Exponential and Logarithmic Equations 

5.6, Applications from Business, Finance, and Science 

5.7, Exponential, Logarithmic, and Logistic Equation Models 

Chapter 6: Introduction to Trigonometry 

6.1, Angle Measure, Special Triangles, and Special Angles 

6.2, Unit Circles and the Trigonometry of Real Numbers 

6.3, Graphs of Sine and Cosine Functions 

6.4, Graphs of the Cosecant, Secant, Tangent, and Cotangent Functions 

6.5, Transformations and Applications of Trigonometric Graphs 

6.6, The Trigonometry of Right Triangles 

6.7, Trigonometry and the Coordinate Plane 

6.8, Trigonometric Equation Models 


7.1, Fundamental Identities and Families of Identities 

7.2, More on Verifying Identities 

7.3, The Sum and Difference Identities 

7.4, The Double-Angle, Half-Angle and Product-to-Sum Identities 

7.5, The Inverse Trigonometric Functions and their Applications 

7.6, Solving Basic Trig Equations 

7.7, General Trig Equations and Applications 


8.1, Oblique Triangles and the Law of Sines 

8.2, The Law of Cosines; the Area of a Triangle 

8.3, Vectors and Vector Diagrams 

8.4, Vector Applications and the Dot Product 

8.5, Complex Numbers in Trigonometric Form 

8.6, De Moivre’s Theorem and the Theorem on nth Roots 

Chapter 9: Systems of Equations ad Inequalities; Matrices 

9.1, Linear Systems in Two Variables with Applications 

9.2, Linear Systems in Three Variables with Applications 

9.3, Systems of Inequalities and Linear Programming 

9.4, Partial Fraction Decomposition 

9.5, Solving Linear Systems Using Matrices and Row Operations 

9.6, The Algebra of Matrices 

9.7, Solving Linear Systems Using Matrix Equations 

9.8, Applications of Matrices and Determinants: Cramer’s Rule, 

Geometry, and More 

Chapter 10: Analytical Geometry; Polar and Parametric Equations 

10.1, A Brief Introduction to Analytic Geometry 

10.2, The Circle and the Ellipse 

10.3, The Hyperbola 

10.4, The Analytic Parabola 

10.5, Nonlinear Systems of Equations and Inequalities 

10.6, Polar Coordinates, Equations, and Graphs 

10.7, More on the Conic Sections: Rotation of Axes and Polar Form 

10.8, Parametric Equations and Graphs 

Chapter 11: Sequences, Series, Counting, and Probability 

11.1, Sequences and Series 

11.2, Arithmetic Sequences 

11.3, Geometric Sequences 

11.4, Mathematical Induction 

11.5, Counting Techniques 

11.6, Introduction to Probability 

11.7, The Binomial Theorem 

Chapter 12: Bridges to Calculus – An Introduction to Limits 

12.1, Finding Limits Numerically and Graphically 

12.2, Algebraic Methods for Finding Limits; One-Sided Limits and 

Continuity 

12.3, Infinite Limits and Limits at Infinity 

12.4, Applications of Limits: Instantaneous Rates of Change and the 

Area Under a Curve 

Appendix A: A Review of Basic Concepts and Skills 

A.1, Algebraic Expressions and the Properties of Real Numbers 

A.2, Exponents, Scientific Notation, and a Review of Polynomials 

A.3, Solving Linear Equations and Inequalities 

A.4, Factoring Polynomials and Solving Equations by Factoring 

A.5, Rational Expressions and Equations 

A.6, Radicals, Rational Exponents, and Radical Equations 

Appendix B: Proof Positive! 

Appendix C: More on Synthetic Division 

Appendix D: Reduced Row-Echelon Form and More on Matrices 

Appendix E: The Equation of a Conic 

68

Precalculus 

Appendix F: Sinusoidal Regression Models 

Online Appendices 

AO.1, The Language, Notation, and Numbers of Mathematics 

AO.2, Geometry Review with Unit Conversions 


NEW *9780077349912* 

PRECALCULUS 

7th Edition 

By Raymond Barnett 

2011 (January 2010) / 944 pages 

ISBN: 9780077349912 

ISBN: 9780071221764 [IE] 


The Barnett, Ziegler, Byleen, and Sobecki College Algebra series is 

designed to be user friendly and to maximize student comprehension 

by emphasizing computational skills, ideas, and problem solving 

as opposed to mathematical theory. Suitable for either one or two 

semester college algebra with trigonometry or precalculus courses, 

Precalculus introduces a unit circle approach to trigonometry and 

includes a chapter on limits to provide students with a solid foundation 

for calculus concepts. The large number of pedagogical devices employed 

in this text will guide a student through the course. Integrated 

 

boxes which encourage students to think critically about mathematical 

concepts. In each section, the worked examples are followed by 

matched problems that reinforce the concept being taught. In addition, 

the text contains an abundance of exercises and applications that will 

convince students that math is useful. A MathZone site featuring algorithmic 

exercises, videos, and other resources accompanies the text. 

FEATURES 

Appealing Visuals: The design has been completely updated 

in full color and now offers a more contemporary and inviting visual 

backdrop for the concepts. Photos have been added to enhance the 

text and contribute to the updated appearance. 

Preview of Calculus: New to this edition, a chapter on limits is 

offered on the MathZone site for this text. “Foundations of Calculus” 

icons are included throughout the text to identify key examples and 

exercises needed to build a solid skill set for calculus. 

Examples and Matched Problems: Detailed worked examples 

-- now with expanded color notes for students that outline the solution 

steps in words -- appear frequently throughout the sections to introduce 

concepts and demonstrate problem-solving techniques. Each 

example is followed by a Matched Problem to help students solidify 

their understanding and play an active role in the learning process. 

For easy reference, answers to the Matched Problems appear at the 

end of each section. 

Technological Support: New “Technology Connections” boxes 

integrated at appropriate points in the text illustrate how techniques 

previously introduced in an algebraic context may be solved using 

a graphing calculator. Students always learn the algebraic methods 

first so that they develop a solid grasp of these methods and do not 

become calculator-dependent. The exercise sets contain calculatorbased 

exercises that are clearly marked with a calculator icon. The 

use of technology is completely optional with this text. All technology 

features and exercises may be omitted without sacrificing content 

coverage. 

Exploration and Discussion: Integrated at appropriate places 

in each section, Explore/Discuss boxes encourage students to think 

critically about mathematics. These features also provide excellent 

opportunities for group work. 

Balanced Exercise Sets: The exercise sets at the end of each 

section and chapter contain a mix of skill exercises, calculator exercises, 

reasoning and writing exercises, and applied exercises. The 

exercises are graded by difficulty level, becoming progressively harder 

as students gain confidence in their skills. However, the old A/B/C 

subdivisions have been omitted so that students will not be daunted 

by seeing problems labeled as being more difficult. These subdivisions 

may be found in the Instructor’s Solutions Manual. 

Opportunities for Reviewing and Expanding Knowledge: Chapter 

Review sections at the end of each chapter provide a thorough 

review of the important terms and topics in the chapter. Following 

this recap is a comprehensive set of Chapter Review Exercises. 

Cumulative Review Exercises appear every two or three chapters 

for additional reinforcement. Every chapter contains a Group Activity 

that allows students to work with classmates to explore chapter 

topics in greater detail. 

Objective-Based Learning: Introductory section objectives help 

provide a road map through the topics of the section. The Chapter 

Reviews are organized by section objective. 

CONTENTS 



R-2 Exponents and Radicals 

R-3 Polynomials: Basic Operations and Factoring 













2-1 Rectangular Coordinates 







3-1 Functions 




















69

Precalculus 








CHAPTER 6: TRIGONOMETRIC FUNCTIONS 



6-3 Solving Right Triangles 

6-4 Trigonometric Functions: Properties and Graphs 

6-5 More General Trigonometric Functions 





CHAPTER 7: TRIGONOMETRIC IDENTITIES AND CONDITIONAL 

EQUATIONS 






Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin(Bt + C) - A 

Harmonic Analysis Tool 


CHAPTER 8: ADDITIONAL TOPICS IN TRIGONOMETRY 











9-2 Ellipse 

9-3 Hyperbola 





MATRICES 






Chapter 10 Group Activity: Modeling with Systems of Linear Equations 









11-4 Counting Techniques: Multiplication Principle, Permutations, 

and Combinations 




Formulas 


9. 10, & 11 Cumulative Review Exercises 

CHAPTER 12: LIMITS: AN INTRODUCTION TO CALCULUS 












APPENDIX B 



PRECALCULUS 

2nd Edition 

By John W. Coburn, Saint Louis Community College--Florissant Valley 


ISBN: 9780077276508 

ISBN: 9780070172982 [IE] 



 







appropriate for college algebra level students, Coburn’s Precalculus 

uses narrative, extensive examples, and a range of exercises to 

connect seemingly disparate mathematical topics into a cohesive 




 

students across the country, Precalculus second edition, continues 




CONTENTS 




























70

Precalculus 




Equations 



Chapter 5: Introduction to Trigonometric Functions 

5-1 Angle Measure, Special Triangles, and Special Angles 

5-2 Unit Circles and the Trigonometry of Real Numbers 

5-3 Graphs of Sine and Cosine Functions; Cosecant and Secant 

Functions 

5-4 Graphs of Tangent and Cotangent Functions 

5-5 Transformations and Applications of Trigonometric Graphs 

5-6 The Trigonometry of Right Triangles 

5-7 Trigonometry and the Coordinate Plane 


6-1 Fundamental Identities and Families of Identities 

6-2 Constructing and Verifying Identities 

6-3 The Sum and Difference Identities 

6-4 Double Angle, Half Angle & Product-to-Sum Identities 

6-5 The Inverse Trigonometric Functions and Their Applications 

6-6 Solving Basic Trigonometric Equations 

6-7 General Trigonometric Equations and Applications 


7-1 Oblique Triangles and the Law of Sines 

7-2 The Law of Cosines; Area of a Triangle 

7-3 Vectors and Vector Diagrams 

7-4 Vector Applications and the Dot Product 

7-5 Complex Numbers in Trigonometric Form 

7-6 Demoivre’s Theorem and the Theorem on nth Roots 




8-3 Partial Fraction Decomposition 





8-8 Applications of Matrices and Determinants: Cramer’s Rule, Geometry, 

and More 

Chapter 9: Analytical Geometry 






9-6 Polar Coordinates, Equations, and Graphs 

9-7 More on Conic Sections: Rotation of Axes and Polar Form 

9-8 Parametric Equations and Graphs 








10-7 The Binomial Theorem 

Chapter 11: Bridges to Calculus--An Introduction to Limits 

11-1 Finding Limits Numerically and Graphically 

11-2 Algebraic Methods for Finding Limits; One-Sided Limits and 

Continuity 

11-3 Infinite Limits and Limits at Infinity 

11-4 Applications of Limits: Instantaneous Rates of Change and the 

Area Under a Curve 

APPENDICES 

A-1 A Review of Basic Concepts and Skills 

A-2 US Standard Units and the Metric System 

A-3 Rational Expressions and the Least Common Denominator 




PRECALCULUS: GRAPHS AND MODELS 

3rd Edition 

By Raymond A Barnett, Merritt College, Michael R Ziegler and Karl 

E Byleen of Marquette University, David Sobecki, Miami University- 

Hamilton 


ISBN: 9780077221294 


The Barnett Graphs & Models series in college algebra and 

precalculus maximizes student comprehension by emphasizing 

computational skills, real-world data analysis and modeling, and 

problem solving rather than mathematical theory. Many examples 

feature side-by-side algebraic and graphical solutions, and each is 

followed by a matched problem for the student to work. This active 

involvement in the learning process helps students develop a more 

thorough understanding of concepts and processes. A hallmark of 

the Barnett series, the function concept serves as a unifying theme. 

A major objective of this book is to develop a library of elementary 

functions, including their important properties and uses. Employing 

this library as a basic working tool, students will be able to proceed 

 

 

to analyze the graph and use it to solve the problem. Applications 

included throughout the text give the student substantial experience 

in solving and modeling real world problems in an effort to convince 

even the most skeptical student that mathematics is really useful. 

CONTENTS 

CHAPTER 1 FUNCTIONS, GRAPHS, AND MODELS 

1-1 Using Graphing Utilities 

1-2 Functions 

1-3 Functions: Graphs and Properties 

1-4 Functions: Graphs and Transformations 




Chapter 1 Group Activity: Mathematical Modeling–Choosing a Long 


CHAPTER 2 MODELING WITH LINEAR AND QUADRATIC FUNC- 

TIONS 

2-1 Linear Functions 




2-5 Quadratic Equations and Models 

2-6 Additional Equation Solving Techniques 

2-7 Solving Inequalities 


Chapter 2 Group Activity: Mathematical Modeling in Population 

Studies 


CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS 


3-2 Polynomial Division 







CHAPTER 4 MODELING WITH EXPONENTIAL AND LOGARITHMIC 

FUNCTIONS 







Cumulative Review Chapters 3 and 4 



CHAPTER 5 TRIGONOMETRIC FUNCTIONS 

71

Precalculus 




5-4 Properties of Trigonometric Functions 

5-5 More General Trigonometric Functions and and Models 





CHAPTER 6 TRIGONOMETRIC IDENTITIES AND CONDITIONAL 

EQUATIONS 







Chapter 6 Group Activity: From M sin Bt + N cos Bt to A sin 

(Bt + C)--A Harmonic Analysis Tool 

CHAPTER 7 ADDITIONAL TOPICS IN TRIGONOMETRY 








Cumulative Review Exercise for Chapters 5, 6, and 7 

CHAPTER 8 MODELING WITH SYSTEMS OF EQUATIONS AND 

INEQUALITIES 






Chapter 8 Group Activity: Modeling with Systems of Equations 

CHAPTER 9 MATRICES AND DETERMINANTS 

9-1 Matrix Solutions to Linear Systems 


9-3 Inverse of a Square Matrix 

9-4 Matrix Equations and Systems of Linear Equations 

9-5 Determinants 

9-6 Properties of Determinants 



Chapter 9 Group Activity: Using Matrices to Find Cost, Revenue, 

and Profit 


CHAPTER 10 SEQUENCES, INDUCTION, PROBABILITY 









Formulas 

CHAPTER 11 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY 


11-2 Ellipse 

11-3 Hyperbola 






Appendix A BASIC ALGEBRA REVIEW 

A-1 Algebra and Real Numbers 

A-2 Exponents 

A-3 Radicals 

A-4 Polynomials: Basic Operations 

A-5 Polynomials: Factoring 

A-6 Rational Expressions: Basic Operations 

A-7 Linear Equations and Inequalities 

A-8 Cartesian Coordinate System 

A-9 Basic Formulas in Analytic Geometry 

Appendix A Review 

Appendix A Group Activity: Rational Number Representations 

Appendix B Special Topics 

B-1 Significant Digits 

B-2 Partial Fractions 

B-3 Parametric Equations 

Appendix C Geometric Formulas 

PRECALCULUS WITH LIMITS 

6th Edition 

By Raymond A Barnett, Merritt College, Michael R Ziegler and Karl E 

Byleen of Marquette University 

2008 (March 2007) / Hardcover 

ISBN: 9780073365800 (GOP) 


The Barnett, Ziegler, Byleen College Algebra series is designed to be 

user friendly and to maximize student comprehension, emphasizing 

computational skills, ideas, and problem solving as opposed to mathematical 

theory. Suitable for a one or two semester college algebra 

with trigonometry or precalculus course, Precalculus with Limits introduces 

a unit circle approach to trigonometry and includes a chapter on 

limits to provide students with a solid foundation for calculus concepts. 

The large number of pedagogical devices employed in this text will 

guide a student through the course. Integrated throughout the text, 

 

age students to think critically about mathematical concepts. In each 

section, the worked examples are followed by matched problems that 

reinforce the concept being taught. In addition, the text contains an 

abundance of exercises and applications that will convince students 

that math is useful. A MathZone site featuring algorithmic exercises, 

videos, and other resources accompanies the text. 

CONTENTS 

Chapter R: Basic Algebraic Operations 


R-2 Exponents 

R-3 Radicals 

R-4 Polynomials: Basic Operations 

R-5 Polynomials: Factoring 



Chapter R Review Exercises 

Chapter R Group Activity: Rational and Irrational Numbers 




1-3 Absolute Value in Equations and Inequalities 



1-6 Additional Equation-Solving Techniques 




Chapter 2: Graphs 

2-1 Cartesian Coordinate System 







Chapter 3: Functions 

72

Precalculus 

3-1 Functions 








Chapter 3 Group Activity: Mathematical Modeling: Choosing a Long- 


Cumulative Review Exercises Chapters 1-3 

Chapter 4: Polynomials and Rational Functions 

4-1 Polynomial Functions and Models 






















6-4 Properties of Trigonometric Functions 

6-5 More General Trigonometric Functions and Models 






Chapter 7: Trigonometric Identities and Conditional Equations 








Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin (Bt + C): 

A Harmonic Analysis Tool 

Chapter 8: Additional Topics in Trigonometry 










Chapter 9: Additional Topics in Analytic Geometry 

9-1 Conic Sections; Parabolas 

9-2 Ellipse 

9-3 Hyperbola 

9-4 Translation and Rotation of Axes 




Chapter 10: Systems of Equations and Inequalities; Matrices 



10-3 Systems of Linear Equations: Gauss-Jordan Elimination 


10-5 Systems of Linear Equations: Matrix Inverse Methods 


10-7 Systems of Linear Inequalities in Two Variables 




Chapter 10 Group Activity: Modeling With Systems of Linear Equations 

Chapter 11: Sequences, Induction, and Probability 










Formulas 


Chapter 12 Limits: An Introduction to Calculus 









Appendix A: Special Topics A-1 Scientific Notation and Significant 

Digits A-2 Partial Fractions A-3 Parametric Equations 

Appendix B: Geometric Formulas Student Answers Subject Index 

SCHAUM’S OUTLINE OF BEGINNING 

CALCULUS 

3rd Edition 


2010 (August 2009) / 416 pages 

ISBN: 9780071635356 

Fortunately for you, there’s Schaum’s Outlines. More than 40 million 

students have trusted Schaum’s to help them succeed in the 

classroom and on exams. Schaum’s is the key to faster learning 

and higher grades in every subject. Each Outline presents all the 

essential course information in an easy-to-follow, topic-by-topic 

format. You also get hundreds of examples, solved problems, and 

practice exercises to test your skills. 

This Schaum’s Outline gives you: 

Practice problems with full explanations that reinforce knowledge 

• Coverage of the most up-to-date developments in your course field 

• In-depth review of practices and applications 

• Fully compatible with your classroom text, Schaum’s highlights all 

the important facts you need to know. Use Schaum’s to shorten 

your study time-and get your best test scores! 

Schaum’s Outlines-Problem Solved. 

CONTENTS 

1. Coordinate Systems on a Line 

2. Coordinate Systems in a Plane 

3. Graphs of Equations 

4. Straight Lines 

5. Intersections of Graphs 

6. Symmetry 

7. Functions and Their Graphs 

73

Precalculus 

8. Limits 

9. Special Limits 

10. Continuity 

11. The Slope of a Tangent Line 

12. The Derivative 

13. More on the Derivative 

14. Maximum and Minimum Problems 

15. The Chain Rule 

16. Implicit Differentiation 

17. The Mean-Value Theorem and the Sign of the Derivative 

18. Rectilinear Motion and Instantaneous Velocity 

19. Instantaneous Rate of Change 

20. Related Rates 

21. Approximation by Differentials; Newton’s Method 

22. Higher-Order Derivatives 

23. Applications of the Second Derivative and Graph Sketching 

24. More Maximum and Minimum Problems 

25. Angle Measure 

26. Sine and Cosine Functions 

27. Graphs and Derivatives of Sine and Cosine Functions 

28. The Tangent and Other Trigonometric Functions 

29. Antiderivatives 

30. The Definite Integral 

31. The Fundamental Theorem of Calculus 

32. Applications of Integration I: Area and Arc Length 

33. Applications of Integration II: Volume 

34. The Natural Logarithm 

35. Exponential Functions 

36. L’Hopital’s Rule: Exponential Growth and Decay 

37. Inverse Trigonometric Functions 

38. Integration by Parts 

39. Trigonometric Integrands and Trigonometric Substitutions 

40. Integration of Rational Function: The Method of Partial Fractions 

22. Trigonometric Identities and Equations 

23. Sum, Difference, Multiple, and Half-Angle Formulas 


25. Triangles 

26. Vectors 

27. Polar Coordinates; Parametric Equations 

28. Trigonometric Form of Complex Numbers 

29. Systems of Linear Equations 

30. Gaussian and Gauss-Jordan Elimination 

31. Partial Fraction 

32. Decomposition 

33. Non-Linear Systems of Equations 

34. Introduction to Matrix Algebra 

35. Matrix Multiplication and Inverses 

36. Determinants and Cramer’s Rule 

37. Loci; Parabolas 

38. Ellipses and Hyperbolas 

39. Rotation of Axes 


41. Sequences and Series 

42. The Principle of Mathematical Induction 

43. Special Sequences and Series 

44. The Binomial Theorem 


SCHAUM’S OUTLINE OF PRECALCULUS 

2nd Edition 

 

2009 (July 2008) / 426 pages / Softcover 

ISBN: 9780071508643 




thousands of college and high school students who enroll in precalculus 

courses. 

CONTENTS 

1. Polynomials 

2. Exponents 

3. Rational and Radical Expressions 

4. Linear and Non-Linear Equations 

5. Linear and Non-Linear Inequalities 

6. Absolute Value in Equations and Inequalities 

7. Analytic Geometry 

8. Functions 

9. Linear Functions 

10. Transformations and Graphs 

11. Quadratic Functions 

12. Algebra of Functions 

13. Polynomial Functions 

14. Rational Functions 

15. Algebraic Functions; Variations 

16. Exponential Functions 

17. Logarithmic Functions 

18. Exponential and Logarithmic Equations 

19. Trigonometric Functions 

20. Graphs of Trignometric Functions 

21. Angles 

PRE-CALCULUS DEMYSTIFIED 

By Rhonda Huettenmueller 

2005 / 468 pages 

ISBN: 9780071439275 


CONTENTS 

Preface 

Chapter 1: The Slope and Equation of a Line 

Chapter 2: Introduction to Functions 

Chapter 3: Functions and Their Graphs 

Chapter 4: Combinations of Functions and Inverse Functions 

Chapter 5: Translations and Special Functions 

Chapter 6: Quadratic Functions 

Chapter 7: Polynomial Functions 

Chapter 8: Rational Functions 

Chapter 9: Exponents and Logarithms 


Chapter 11: Matrices 

Chapter 12: Conic Sections 

Chapter 13: Trigonometry 

Chapter 14: Sequences and Series 

Appendix 

Final Exam 

74

Precalculus 

BOB MILLER’S CALC FOR THE CLUELESS: 

PRECALC 

3rd Edition 


2005 / 208 pages 

ISBN: 9780071453172 


CONTENTS 

Acknowledgements 

To the student 

CHAPTER 1 Lines, the Straight Kind 

CHAPTER 2 Quadratic Equations 

CHAPTER 3 Inequalities, Linear and quadratic 

CHAPTER 4 Absolute Value 

CHAPTER 5 Exponents--Negative, Fractional 

CHAPTER 6 Geometric Formulas and Facts You must Know 

CHAPTER 7 Distances, Midpoints, Circles and Parabolas 

CHAPTER 8 Functions 

CHAPTER 9 Linear Systems and More About y=x2 

CHAPTER 10 Trigonometry 

CHAPTER 11 Curve Sketching 

CHAPTER 12 Modern Logaraithims 

CHAPTER 13 Parabolas II, Ellipses, and Hyperbolas 

CHAPTER 14 Writing Fumctions of x, the Algerbraic Part of Calculus 

Word Problems 

CHAPTER 15 The Binomial Theorem 

CHAPTER 17Finite Induction 

CHAPTER 18 Progressions 

CHAPTER 19 Limits 

APPENDIX Synthetic Division and Sets 

INDEX 

About Bob Miller... In His Own Words 




 




REVIEW COPY 










75

Precalculus 

76

Applied / Business Calculus ...............................................................................79 


Calculus and Analytic Geometry.........................................................................81 


Multi-Variable Calculus .......................................................................................93 


CALCULUS 

Single Variable Calculus .....................................................................................87 


77

New Titles 

CALCULUS 


Calculus, 4e Smith 9780073383118 81 

Calculus: Early Transcendental Functions, 4e Smith 9780073532325 82, 87, 

93 

78

Calculus 

Applied / Business Calculus 


APPLIED CALCULUS FOR BUSINESS, 

ECONOMICS, AND THE SOCIAL AND LIFE 

SCIENCES 

Expanded Edition, 10th Edition 

By Laurence D. Hoffmann, Salomon Smith Barney, Gerald L. Bradley of 

Claremont McKenna College 

2010 (January 2009) \ Hardcover 

ISBN: 9780077297886 

ISBN: 9780071311816 [IE] 

www.mhhe.com/hoffmann 

Applied Calculus for Business, Economics, and the Social and Life 

Sciences, Expanded Edition provides a sound, intuitive understanding 

of the basic concepts students need as they pursue careers in 

business, economics, and the life and social sciences. Students 

achieve success using this text as a result of the author’s applied and 

real-world orientation to concepts, problem-solving approach, straight 

forward and concise writing style, and comprehensive exercise sets. 

More than 100,000 students worldwide have studied from this text! 

CONTENTS 

Chapter 1: Functions, Graphs, and Limits 

1.1 Functions 

1.2 The Graph of a Function 


1.4 Functional Models 

1.5 Limits 

1.6 One-Sided Limits and Continuity 

Chapter 2: Differentiation: Basic Concepts 

1.1 The Derivative 

1.2 Techniques of Differentiation 

1.3 Product and Quotient Rules; Higher-Order Derivatives 

1.4 The Chain Rule 

1.5 Marginal Analysis and Approximations Using Increments 

1.6 Implicit Differentiation and Related Rates 

Chapter 3: Additional Applications of the Derivative 

3.1 Increasing and Decreasing Functions; Relative Extrema 

3.2 Concavity and Points of Inflection 

3.3 Curve Sketching 

3.4 Optimization; Elasticity of Demand 

3.5 Additional Applied Optimization 


4.1 Exponential Functions: Continuous Compounding 


4.3 Applications; Exponential Models 

Chapter 5: Integration 

5.1 Antidifferentiation: The Indefinite Integral 

5.2 Integration by Substitution 

5.3 The Definite Integral and the Fundamental Theorem of Calculus 

5.4 Applying Definite Integration: Area Between Curves and Average 

Value 

5.5 Additional Applications to Business and Economics 

5.6 Additional Applications to the Life and Social Sciences 

Chapter 6: Additional Topics in Integration 

6.1 Integration by Parts; Integral Tables 

6.2 Improper Integrals 

6.3 Numerical Integration 

Chapter 7: Calculus of Several Variables 

7.1 Functions of Several Variables 

7.2 Partial Derivatives 

7.3 Optimizing Functions of Two Variables 

7.4 The Method of Least-Squares 

7.5 Constrained Optimization: The Method of Lagrange Multipliers 

7.6 Double Integrals 

Chapter 8: Differential Equations 

8.1 Introduction to Differential Equations 

8.2 First-Order Linear Differential Equations 

8.3 Additional Applications of Differential Equations 

8.4 Approximate Solutions of Differential Equations 

8.5 Difference Equations; The Cobweb Model 

Chapter 9: Infinite Series and Taylor Series Approximations 

9.1 Infinite Series; Geometric Series 

9.2 Tests for Convergence 

9.3 Functions as Power Series; Taylor Series 

Chapter 10: Probability and Calculus 

10.1 Introduction to Probability; Discrete Random Variables 

10.2 Continuous Random Variables 

10.3 Expected Value and Variance of Continuous Random Variables 

10.4 Normal and Poisson Probability Distributions 


11.1 The Trigonometric Functions 

11.2 Differentiation and Integration of Trigonometric Functions 

11.3 Additional Applications Involving Trigonometric Function 

Appendix A: Algebra Review 

A.1 A Brief Review of Algebra 

A.2 Factoring Polynomials and Solving Systems of Equations 

A.3 Evaluating Limits with L’Hopital’s Rule 

A.4 The Summation Notation 


CALCULUS FOR BUSINESS, ECONOMICS, 

AND THE SOCIAL AND LIFE SCIENCES 

Brief Edition, 10th Edition 

By Laurence D. Hoffmann, Salomon Smith Barney, Gerald L. Bradley of 

Claremont McKenna College 

2010 (January 2009) / Hardcover 

ISBN: 9780077292737 

ISBN: 9780071288903 [IE] 

www.mhhe.com/hoffman 

Calculus for Business, Economics, and the Social and Life Sciences, 

Brief Edition introduces calculus in real-world contexts and provides 

a sound, intuitive understanding of the basic concepts students need 

as they pursue careers in business, the life sciences, and the social 

sciences. Students achieve success using this text as a result of the 

authors’ applied and real-world orientation to concepts, problemsolving 

approach, straightforward and concise writing style, and 

comprehensive exercise sets. More than 100,000 students worldwide 

have studied from this text! 

CONTENTS 

Chapter 1: Functions, Graphs, and Limits 

1.1 Functions 

1.2 The Graph of a Function 


1.4 Functional Models 

1.5 Limits 

1.6 One-Sided Limits and Continuity 

Chapter 2: Differentiation: Basic Concepts 

2.1 The Derivative 

2.2 Techniques of Differentiation 

2.3 Product and Quotient Rules; Higher-Order Derivatives 


2.5 Marginal Analysis and Approximations Using Increments 

2.6 Implicit Differentiation and Related Rates 

Chapter 3: Additional Applications of the Derivative 

3.1 Increasing and Decreasing Functions; Relative Extrema 

3.2 Concavity and Points of Inflection 

3.3 Curve Sketching 

79

Calculus 

3.4 Optimization; Elasticity of Demand 

3.5 Additional Applied Optimization 


4.1 Exponential Functions: Continuous Compounding 


4.3 Applications; Exponential Models 


5.1 Antidifferentiation: The Indefinite Integral 


5.3 The Definite Integral and the Fundamental Theorem of Calculus 

5.4 Applying Definite Integration: Area Between Curves and Average 

Value 

5.5 Additional Applications to Business and Economics 

5.6 Additional Applications to the Life and Social Sciences 

Chapter 6: Additional Topics in Integration 

6.1 Integration by Parts; Integral Tables 

6.2 Introduction to Differential Equations 

6.3 Improper Integrals; Continuous Probability 

6.4 Numerical Integration 

Chapter 7: Calculus of Several Variables 



7.3 Optimizing Functions of Two Variables 

7.4 The Method of Least-Squares 

7.5 Constrained Optimization: The Method of Lagrange Multipliers 



A.1 A Brief Review of Algebra 

A.2 Factoring Polynomials and Solving Systems of Equations 

A.3 Evaluating Limits with L’Hopital’s Rule 

A.4 The Summation Notation 


BUSINESS CALCULUS DEMYSTIFIED 

By Rhonda Huettenmueller, University of North Texas 

2006 / 384 pages 

ISBN: 9780071451574 


CONTENTS 

Chapter 1: Algebra Review 

The slope and equation of a line 

Finding x-intercepts 

Solving equations 

Quadratic functions 

The vertex 

The maximum/minimum value of a quadratic function 

Increasing/decreasing intervals 

Some important exponent properties 

Chapter 2: Average rate of change 

Limits 

Chapter 3: Definition of derivative 

Properties of the derivative 

Instantaneous rates of change 

The tangent line 

The Power Rule 

The Product Rule 

The Quotient Rule 

The Chain Rule 

Layering different formulas 

Chapter 5: Applications 

Optimizing functions 

Maximizing revenue and profit, minimizing cost, and other optimizing 

problems 

Chapter 6: The second derivative 

Concavity 

Another method for optimizing functions 

Chapter 7: Implicit differentiation 

Chapter 8: Rational functions 

Limits and asymptotes 

Chapter 9: Using calculus to sketch graphs 

Graphs of polynomial functions 

Chapter 10: Exponents and Logarithm functions 

Using log properties to simplify differentiation 


The antiderivative 

Integration formulas 

The area under the curve 

More integration formulas 

Integration techniques 

Chapter 12: Applications of the integral 

SCHAUM’S OUTLINE OF CALCULUS FOR 

BUSINESS, ECONOMICS, AND THE SOCIAL 

SCIENCES 

By Edward T Dowling, Fordham Univesity 

1990 / 288 pages 

ISBN: 9780070176737 


CONTENTS 

Review. 

Equations and Graphs. 

Functions. 

The Derivative. 

Differentiation. 

Uses of the Derivative. 

Exponential and Logarithmic Functions. 

Integration. 

Multivariate Calculus. 

More of Integration and Multivariate Calculus. 




 




80

Calculus 

Calculus and Analytic 

Geometry 


NEW *9780073383118* 

CALCULUS 

4th Edition 

By Robert Smith, Millersville University and 

Roland Minton, Roanoke College 

2012 (April 2011) / 1376 pages 

ISBN: 9780073383118 

ISBN: 9780071316576 [IE] 

www.mhhe.com/smithminton 

Smith/Minton, Calculus provides students and instructors with a 

mathematically sound text, oustanding exercise sets and an engaging 

writing style that students can actually read. Packaged with ALEKS 

Prep for Calculus, Smith/Minton offers a complete package to ensure 

students success in Calculus. 

FEATURES 

A key goal of the Fourth Edition revision was to offer a clearer 

presentation of calculus. With this goal in mind, the authors were able 

to reduce the amount of material by nearly 150 pages. 

The level of rigor has been carefully balanced to ensure that 

concepts are presented in a rigorously correct manner without allowing 

technical details to overwhelm beginning calculus students. 

The exercise sets were redesigned in an effort to aid instructors 

by allowing them to more easily identify and assign problems of a 

certain type. 

The derivatives of hyperbolic functions are developed in Section 

6.6, giving this important class of functions a full development. 

Separating these functions from the exponential and trigonometric 

functions allows for comprehensive exploration of the relationship 

between these functions, exponential functions, trigonometric functions, 

and their derivatives and integrals. 

More than 1,000 new classic calculus problems were added, 

covering topics from polynomials to multivariable calculus, including 

optimization, related rates, integration techniques and applications, 

parametric and polar equations, vectors, vector calculus, and differential 

equations. 

A reorganization of the exercise sets makes the range of available 

exercises more transparent. Earlier exercises focus on fundamentals, 

as developed in examples in the text. Later exercises explore interesting 

extensions of the material presented in the text. 

Multi-step exercises help students make connections among concepts 

and require students to become more critical readers. Closely 

related exercises are different parts of the same numbered exercise, 

with follow-up questions to solidify lessons learned. 

Application exercises have been separated out in all appropriate 

sections. A new header identifies the location of applied exercises 

which are designed to show students the connection between what 

they learn in class, other areas of study, and outside life. This differentiates 

the applications from exploratory exercises that allow students 

to discover connections and extensions for themselves. 

The unique variety of exercises has been enhanced by new 

design elements. The reorganization of exercises makes it easier to 

access the wide range of available options. 

CONTENTS 

Calculus: Early Transcendental Functions 

Chapter 0: Preliminaries 

0.1, “The Real Numbers and the Cartesian Plane” 

0.2, “Lines and Functions” 

0.3, “Graphing Calculators and Computer Algebra Systems” 

0.4, “Trigonometric Functions” 

0.5, “Transformations of Functions” 

Chapter 1: Limits and Continuity 

1.1, “A Brief Preview of Calculus: Tangent Lines and the Length of 

a Curve 

1.2, “The Concept of Limit” 

1.3, “Computation of Limits” 

1.4, “Continuity and Its Consequences” 

1.5, “Limits Involving Infinity; Asymptotes” 

1.6, “Formal Definition of the Limit” 

1.7, “Limits and Loss-of-Significance Errors” 

Chapter 2: Differentiation 

2.1, “Tangent Lines and Velocity” 

2.2, “The Derivative” 

2.3, “Computation of Derivatives: The Power Rule” 

2.4, “The Product and Quotient Rules” 

2.5, “The Chain Rule” 

2.6, “Derivatives of Trigonometric Functions” 

2.7, “Implicit Differentiation” 

2.8, “The Mean Value Theorem” 

Chapter 3: Applications of the Derivative 

3.1, “Linear Approximations and Newton’s Method”” 

3.2, “Maximum and Minimum Values” 

3.3, “Increasing and Decreasing Functions” 

3.4, “Concavity and the Second Derivative Test” 

3.5, “Overview of Curve Sketching” 

3.6, “Optimization” 

3.7, “Related Rates” 

3.8, “Rates of Change in Economics and the Sciences” 


4.1, “Antiderivatives” 

4.2, “Sums and Sigma Notation” 

4.3, “Area” 

4.4, “The Definite Integral” 

4.5, “The Fundamental Theorem of Calculus” 

4.6, “Integration by Substitution” 

4.7, “Numerical Integration” 

Chapter 5: Applications of the Definite Integral 

5.1, “Area Between Curves” 

5.2, “Volume: Slicing, Disks and Washers” 

5.3, “Volumes by Cylindrical Shells” 

5.4, “Arc Length and Surface Area” 

5.5, “Projectile Motion” 

5.6, “Applications of Integration to Physics and Engineering” 

Chapter 6: Exponentials, Logarithms and Other Transcendental 

Functions 

6.1, “The Natural Logarithm” 

6.2, “Inverse Functions” 

6.3, “The Exponential Function” 

6.4, “The Inverse Trigonometric Functions” 

6.5, “The Calculus of the Inverse Trigonometric Functions” 

6.6, “The Hyperbolic Functions” 

Chapter 7: Integration Techniques 

7.1, “Review of Formulas and Techniques” 

7.2, “Integration by Parts” 

7.3, “Trigonometric Techniques of Integration” 

7.4, “Integration of Rational Functions Using Partial Fractions” 

81

Calculus 

7.5, “Integration Tables and Computer Algebra Systems” 

7.6, “Improper Integrals” 

57.7, “Probability” 

Chapter 8: First-Order Differential Equations 

8.1, “Modeling with Differential Equations” 

8.2, “Separable Differential Equations” 

8.3, “Direction Fields and Euler’s Method” 

8.4, “Systems of First-Order Differential Equations” 

Chapter 9: Infinite Series 

9.1, “Sequences of Real Numbers” 

9.2, “Infinite Series” 

9.3, “The Integral and Comparison Tests” 

9.4, “Alternating Series” 

9.5, “Absolute Convergence and the Ratio Test” 

9.6, “Power Series” 

9.7, “Taylor Series” 

9.8, “Applications of Taylor Series” 

9.9, “Fourier Series” 

Chapter 10: Parametric Equations and Polar Coordinates 

10.1, “Plane curves and Parametric Equations” 

10.2, “Calculus and Parametric Equations” 

10.3, “Arc Length and Surface Area in Parametric Equations” 

10.4, “Polar Coordinates” 

10.5, “Calculus and Polar Coordinates” 

10.6, “Conic Sections” 

10.7, “Conic Sections in Polar Coordinates” 

Chapter 11: Vectors and the Geometry of Space 

11.1, “Vectors in the Plane” 

11.2, “Vectors in Space” 

11.3, “The Dot Product” 

11.4, “The Cross Product” 

11.5, “Lines and Planes in Space” 

11.6, “Surfaces in Space” 

Chapter 12: Vector-Valued Functions 

12.1, “Vector-Valued Functions” 

12.2, “The Calculus of Vector-Valued Functions” 

12.3, “Motion in Space” 

12.4, “Curvature” 

12.5, “Tangent and Normal Vectors” 

12.6, “Parametric Surfaces” 

Chapter 13: Functions of Several Variables and Partial Differentiation 

13.1, “Functions of Several Variables” 

13.2, “Limits and Continuity” 

13.3, “Partial Derivatives” 

13.4, “Tangent Planes and Linear Approximations” 


13.6, “The Gradient and Directional Derivatives” 

13.7, “Extrema of Functions of Several Variables” 

13.8, “Constrained Optimization and and Lagrange Multipliers” 

Chapter 14: Multiple Integrals 

14.1, “Double Integrals” 

14.2, “Area, Volume and Center of Mass” 

14.3, “Double Integrals in Polar Coordinates” 

14.4, “Surface Area” 

14.5, “Triple Integrals” 

14.6, “Cylindrical Coordinates” 

14.7, “Spherical Coordinates” 

14.8, “Change of Variables in Multiple Integrals” 

Chapter 15: Vector Calculus 

15.1, “Vector Fields” 

15.2, “Line Integrals” 

15.3, “Independence of Path and Conservative Vector Fields” 

15.4, “Green’s Theorem” 

15.5, “Curl and Divergence” 

15.6, “Surface Integrals” 

15.7, “The Divergence Theorem” 

15.8, “Stokes’ Theorem” 

15.9, “Applications of Vector Calculus” 

Chapter 16: Second Order Differential Equations 

16.1, Second-Order Equations With Constant Coefficients” 

16.2, “Nonhomogeneous Equations: Undetermined Coefficients” 

16.3, “Applications of Second-Order Equations” 

16.4, “Power Series Solutions of Differential Equations” 

Appendix A: Proofs of Selected Theorems 

Appendix B: Answers to Odd-Numbered Exercises 


NEW *9780073532325* 

CALCULUS 

Early Transcendental Functions, 

4th Edition 



2012 (January 2011) / 1376 pages 

ISBN: 9780073532325 

ISBN: 9780071316569 [IE] 


In Calculus: Early Transcendental Functions, 4e by Robert Smith and 

Roland Minton, the authors combine the best elements of reform with 

the most reliable aspects of mainstream calculus teaching, resulting 

in a motivating, challenging book. Smith/Minton also provide exceptional, 

reality-based applications that appeal to students’ interests and 

demonstrate the elegance of math in the world around us. 

With the CourseSmart eTextbook version of this title, students can 

save up to 50% off the cost of a print book, reduce their impact on 

the environment, and access powerful web tools for learning. Faculty 

can also review and compare the full text online without having to 

wait for a print desk copy. CourseSmart is an online eTextbook, which 

means users need to be connected to the internet in order to access. 

Students can also print sections of the book for maximum portability. 

CONTENTS 



0.1, “Polynomials and Rational Functions” 



0.4, “Trigonometric and Inverse Trigonometric Functions” 

0.5, “Exponential and Logarithmic Functions” 




a Curve 














2.7, “Derivatives of Exponential and Logarithmic Functions” 

2.8, “Implicit Differentiation and Inverse Trigonometric Functions” 




82

Calculus 


3.2, “Indeterminate Forms and L’Hôpital’s Rule “ 











4.3, “Area” 





4.8, “The Natural Logarithm as an Integral” 

























































































CALCULUS: Concepts and Connections 

By Robert T Smith, Millersville University and Roland B Minton, Roanoke 

College 

2006 / 1,312 pages 

ISBN: 9780073309293 (GOP) 


ISBN: 9780071249027 [IE without MathZone] 


CONTENTS 

Chapter 0: Preliminaries: 

Polynomial and Rational Functions. 

Graphing Calculators and Computer Algebra Systems. 

Inverse Functions. 

Trigonometric and Inverse Trigonometric Functions. 

Exponential and Logarithmic Functions. 

Parametric Equations and Polar Coordinates. 

Chapter 1: Limits and Continuity: 

Preview of Calculus. 

The Concept of Limit. 

Computation of Limits. 

Continuity and its Consequences. 

Method of Bisections. 

Limits Involving Infinity. 

Limits and Loss-of-Significance Errors. 

Chapter 2: Differentiation: 

Tangent Lines and Velocity. 

The Derivative. 

Computation of Derivatives: The Power Rule. 

The Product and Quotient Rules. 

The Chain Rule. 

83

Calculus 

Derivatives of Trigonometric and Inverse Trigonometric Functions. 

Derivatives of Exponential and Logarithmic Functions. 

Implicit Differentiation and Related Rates. 

The Mean Value Theorem. 

Chapter 3: Applications of Differentiation: 

Linear Approximations and Newton’s Method. 

Indeterminate Forms and L’Hopital’s Rule. 

Maximum and Minimum Values. 

Increasing and Decreasing Functions. 

Concavity and Overview of Curve Sketching. 

Optimization. 

Rates of Change in Applications. 

Chapter 4: Integration: 

Area under a Curve. 

The Definite Integral. 

Average Value of a Function. 

Antiderivatives. 

The Fundamental Theorem of Calculus. 

Integration by Substitution. 

Trigonometric Techniques of Integration. 

Integration by Parts. 

Other Techniques of Integration. 

Integration Tables and Computer Algebra Systems. 

Numerical Integration. 

Improper Integrals. 

Comparison Test. 

Chapter 5: Applications of the Definite Integral: 

Area Between Curves. 

Volume. 

Slicing, Disks and Washers. 

Arc Length and Surface Area. 

Projectile Motion. 

Work, Moments, and Hydrostatic Force. 

Probability. 

Chapter 6: Differential Equations: 

Growth and Decay Problems. 

Separable Differential Equations. 

Euler’s Method. 

Second Order Equations with Constant Coefficients. 

Nonhomogeneous Equations: Undetermined Coefficients. 

Applications of Differential Equations. 

Chapter 7: Infinite Series: 

Sequences of Real Numbers. 

Infinite Series. 

The Integral Test and Comparison Tests. 

Alternating Series. 

Absolute Convergence and the Ratio Test. 

Power Series. 

Taylor Series. 

Taylor’s Theorem. 

Applications of Taylor Series. 

Fourier Series. 

Power Series Solutions of Differential Equations. 

Chapter 8: Vectors and the Geometry of Space: 

Vectors in the Plane. 

Vectors in Space. 

The Dot Product. 

Components and Projections. 

The Cross Product. 

Lines and Planes in Space. 

Surfaces in Space. 

Chapter 9: Vector-Valued Functions: 

Vector-Valued Functions. 

Parametric Surfaces. 

The Calculus of Vector-Valued Functions. 

Motion in Space. 

Curvature. 

Tangent and Normal Vectors. 

Components of Acceleration, Kepler’s Laws. 

Chapter 10: Functions of Several Variables and Differentiation: 

Functions of Several Variables. 

Limits and Continuity. 

Partial Derivatives. 

Tangent Planes and Linear Approximations. 

The Chain Rule. 

Implicit Differentiation. 

The Gradient and Directional Derivatives. 

Extrema of Functions of Several Variables. 

Constrained Optimization and Lagrange Multipliers. 

Chapter 11: Multiple Integrals: 

Double Integrals. 

Area, Volume and Center of Mass. 

Double Integrals in Polar Coordinates. 

Surface Area. 

Triple Integrals. 

Cylindrical Coordinates. 

Spherical Coordinates. 

Change of Variables in Multiple Integrals. 

Chapter 12: Vector Calculus: 

Vector Fields. 

Curl and Divergence. 

Line Integrals. 

Independence of Path and Conservative Vector Fields. 

Green’s Theorem. 

Surface Integrals. 

Parametric Representation of Surfaces. 

The Divergence Theorem. 

Stokes’ Theorem. 

Applications of Vector Calculus. 

Appendices: 

A.1 Formal Definition of Limit. 

A.2 Complete Derivation of Derivatives of sin x and cos x. 

A.3 Natural Logarithm Defined as an Integral; Exponential Defined 

as the Inverse of the Natural Logarithm. 

A.4 Hyperbolic Functions. 

A.5 Conic Sections in Polar Coordinates. 

A.6 Proofs of Selected Theorems. 

CALCULUS WITH ANALYTIC GEOMETRY 

2nd Edition 

by George F. Simmons, Colorado College 

1996 / Hardcover / 880 pages 

ISBN: 9780070576421 

CONTENTS 

CHAPTER 1: Numbers, Functions, and Graphs 

1-1 Introduction 

1-2 The Real Line and Coordinate Plane: Pythagoras 

1-3 Slopes and Equations of Straight Lines 

1-4 Circles and Parabolas: Descartes and Fermat 

1-5 The Concept of a Function 

1-6 Graphs of Functions 

1-7 Introductory Trigonometry 

1-8 The Functions Sin O and Cos O 

CHAPTER 2: The Derivative of a Function 

2-0 What is Calculus ? 

2-1 The Problems of Tangents 

2-2 How to Calculate the Slope of the Tangent 

2-3 The Definition of the Derivative 

2-4 Velocity and Rates of Change: Newton and Leibriz 

2-5 The Concept of a Limit: Two Trigonometric Limits 

2-6 Continuous Functions: The Mean Value Theorem and Other 

Theorem 

CHAPTER 3: The Computation of Derivatives 

3-1 Derivatives of Polynomials 

3-2 The Product and Quotient Rules 

3-3 Composite Functions and the Chain Rule 

3-4 Some Trigonometric Derivatives 

3-5 Implicit Functions and Fractional Exponents 

84

Calculus 

3-6 Derivatives of Higher Order 

CHAPTER 4: Applications of Derivatives 

4-1 Increasing and Decreasing Functions: Maxima and Minima 

4-2 Concavity and Points of Inflection 

4-3 Applied Maximum and Minimum Problems 

4-4 More Maximum-Minimum Problems 

4-5 Related Rates 

4-6 Newtons Method for Solving Equations 

4-7 Applications to Economics: Marginal Analysis 

CHAPTER 5: Indefinite Integrals and Differential Equations 


5-2 Differentials and Tangent Line Approximations 

5-3 Indefinite Integrals: Integration by Substitution 

5-4 Differential Equations: Separation of Variables 

5-5 Motion Under Gravity: Escape Velocity and Black Holes 

CHAPTER 6: Definite Integrals 


6-2 The Problem of Areas 

6-3 The Sigma Notation and Certain Special Sums 

6-4 The Area Under a Curve: Definite Integrals 

6-5 The Computation of Areas as Limits 

6-6 The Fundamental Theorem of Calculus 

6-7 Properties of Definite Integrals 

CHAPTER 7: Applications of Integration 

7-1 Introduction: The Intuitive Meaning of Integration 

7-2 The Area between Two Curves 

7-3 Volumes: The Disk Method 

7-4 Volumes: The Method of Cylindrical Shells 

7-5 Arc Length 

7-6 The Area of a Surface of Revolution 

7-7 Work and Energy 

7-8 Hydrostatic Force 

PART II 

CHAPTER 8: Exponential and Logarithm Functions 


8-2 Review of Exponents and Logarithms 

8-3 The Number e and the Function y = e x 

8-4 The Natural Logarithm Function y = ln x 

8-5 Applications 

Population Growth and Radioactive Decay 

8-6 More Applications 

CHAPTER 9: Trigonometric Functions 

9-1 Review of Trigonometry 

9-2 The Derivatives of the Sine and Cosine 

9-3 The Integrals of the Sine and Cosine 

9-4 The Derivatives of the Other Four Functions 

9-5 The Inverse Trigonometric Functions 

9-6 Simple Harmonic Motion 

9-7 Hyperbolic Functions 

CHAPTER 10 : Methods of Integration 


10-2 The Method of Substitution 

10-3 Certain Trigonometric Integrals 

10-4 Trigonometric Substitutions 

10-5 Completing the Square 

10-6 The Method of Partial Fractions 

10-7 Integration by Parts 

10-8 A Mixed Bag 

10-9 Numerical Integration 

CHAPTER 11: Further Applications of Integration 

11-1 The Center of Mass of a Discrete System 

11-2 Centroids 

11-3 The Theorems of Pappus 

11-4 Moment of Inertia 

CHAPTER 12: Indeterminate Forms and Improper Integrals 

12-1 Introduction. The Mean Value Theorem Revisited 

12-2 The Interminate Form 0/0. L’Hospital’s Rule 

12-3 Other Interminate Forms 

12-4 Improper Integrals 

12-5 The Normal Distribution 

CHAPTER 13: Infinite Series of Constants 

13-1 What is an Infinite Series ? 

13-2 Convergent Sequences 

13-3 Convergent and Divergent Series 

13-4 General Properties of Convergent Series 

13-5 Series on Non-negative Terms: Comparison Tests 

13-6 The Integral Test 

13-7 The Ratio Test and Root Test 

13-8 The Alternating Series Test 

CHAPTER 14: Power Series 


14-2 The Interval of Convergence 

14-3 Differentiation and Integration of Power Series 

14-4 Taylor Series and Taylor’s Formula 

14-5 Computations Using Taylor’s Formula 

14-6 Applications to Differential Equations 

14. 7 (optional) Operations on Power Series 

14. 8 (optional) Complex Numbers and Euler’s Formula 

PART III 

CHAPTER 15: Conic Sections 


15-2 Another Look at Circles and Parabolas 

15-3 Ellipses 

15-4 Hyperbolas 

15-5 The Focus-Directrix-Eccentricity Definitions 

15-6 (optional) Second Degree Equations 

CHAPTER 16: Polar Coordinates 

16-1 The Polar Coordinate System 

16-2 More Graphs of Polar Equations 

16-3 Polar Equations of Circles, Conics, and Spirals 

16-4 Arc Length and Tangent Lines 

16-5 Areas in Polar Coordinates 

CHAPTER 17: Parametric Equations 

17-1 Parametric Equations of Curves 

17-2 The Cycloid and Other Similar Curves 

17-3 Vector Algebra 

17-4 Derivatives of Vector Function 

17-5 Curvature and the Unit Normal Vector 

17-6 Tangential and Normal Components of Acceleration 

17-7 Kepler’s Laws and Newton’s Laws of Gravitation 

CHAPTER 18: Vectors in Three-Dimensional Space 

18-1 Coordinates and Vectors in Three-Dimensional Space 

18-2 The Dot Product of Two Vectors 

18-3 The Cross Product of Two Vectors 

18-4 Lines and Planes 

18-5 Cylinders and Surfaces of Revolution 

18-6 Quadric Surfaces 

18-7 Cylindrical and Spherical Coordinates 

CHAPTER 19: Partial Derivatives 

19-1 Functions of Several Variables 

19-2 Partial Derivatives 

19-3 The Tangent Plane to a Surface 

19-4 Increments and Differentials 

19-5 Directional Derivatives and the Gradient 

19-6 The Chain Rule for Partial Derivatives 

19-7 Maximum and Minimum Problems 

19-8 Constrained Maxima and Minima 

19-9 Laplace’s Equation, the Heat Equation, and the Wave Equation 

19-10 (optional) Implicit Functions 

CHAPTER 20: Multiple Integrals 

20-1 Volumes as Iterated Integrals 

20-2 Double Integrals and Iterated Integrals 

20-3 Physical Applications of Double Integrals 

20-4 Double Integrals in Polar Coordinates 

20-5 Triple Integrals 

20-6 Cylindrical Coordinates 

20-7 Spherical Coordinates 

20-8 Areas of curved Surfaces 

CHAPTER 21: Line and Surface Integrals 

21-1 Green’s Theorem, Gauss’s Theorem, and Stokes’ Theorem 

21-2 Line Integrals in the Plane 

21-3 Independence of Path 

21-4 Green’s Theorem 

21-5 Surface Integrals and Gauss’s Theorem 

85

Calculus 

21-6 Maxwell’s Equations : A Final Thought 

Appendices 


SCHAUM’S OUTLINE OF ADVANCED 

CALCULUS 

3rd Edition 

By Robert C Wrede, and Murray R Spiegel (Deceased) 


ISBN: 9780071623667 


Schaum’s Outline of Advanced Calculus mirrors the course in scope 

and sequence to help you understand basic concepts and offer extra 

practice on topics such as derivatives, integrals, multiple integrals, 

applications of partial derivatives, vectors, improper integrals, and 

Fourier series. Coverage will also include linear independence and 

linear dependence of a set of vectors, method of Lagrange multipliers 

for maxima and minima, the divergence theorem, and orthogonality 

conditions for the sine and cosine functions. 

CONTENTS 

1. Numbers 

2. Sequences 

3. Functions, Limits, and Continuity 

4. Derivatives 

5. Integrals 

6. Partial Derivatives 

7. Vectors 

8. Applications of Partial Derivatives 

9. Multiple Integrals 

10. Line Integrals, Surface Integrals, and Integral Theorems 

11. Infinite Series 

12. Improper Integrals 

13. Fourier Series 

14. Fourier Integrals 

15. Gamma and Beta Functions 

16. Functions of a Complex Variable 

SCHAUM’S OUTLINE OF CALCULUS 

5th Edition 

By Frank Ayres and Elliott Mendelson 

2009 (August 2008) / 552 pages 

ISBN: 9780071508612 


This review of standard college courses in calculus has been updated 

 

includes Green’s and Stokes’ theorems, as well as explanations of 

tough topics such as delta-epsilon proofs and Reimann Integrals. 

8. Continuity 


10. Rules for Differentiating Functions 


12. Tangent and Normal Lines 

13. Law of the Mean. Increasing and Decreasing Functions 

14. Maximum and Minimum Values 

15. Curve Sketching. Concavity. Symmetry. 

16. Review of Trigonometry 

17. Differentiation of Trigonometric Functions 


19. Rectilinear and Circular Motion 


21. Differentials. Newton’s Method 


23. The Definite Integral. Area under a Curve 




27. L’Hopital’s Rule 

28. Exponential Growth and Decay 



31. Techniques of Integration I: Integration by Parts 

32. Techniques of Integration II: Trigonometric Integrands and Trigonometric 

Substitutions 

33. Techniques of Integration III: Integration by Partial Fractions 

34. Techniques of Integration IV: Miscellaneous Substitutions 


36. Applications of Integration III: Area of a Surface of Revolution 

37. Parametric Representation of Curves 

38. Curvature 

39. Plane Vectors 

40. Curvilinear Motion 

41. Polar Coordinates 

42. Infinite Sequences 


44. Series with Positive Terms. The Integral Test. Comparison Tests 

45. Alternating Series. Absolute and Conditional Convergence. The 

Ratio Test 

46. Power Series 

47. Taylor and Maclaurin Series. Taylor’s Formulas with Remainder 


49. Total Differential. Differentiability. Chain Rules 

50. Space Vectors 

51. Surfaces and Curves in Space 

52. Directional Derivatives. Maximum and Minimum Values. 

53. Vector Differentiation and Integration 

54. Double and Iterated Integrals 

55. Centroids and Moments of Inertia of Plane Areas 

56. Double Integration Applied to Volume under a Surface and the 

Area of a Curved Surface 

57. Triple Integrals 

58. Masses of Variable Density 

59. Differential Equations of First and Second Order 

CONTENTS 

1. Linear Coordinate Systems. Absolute Value. Inequalities. 

2. Rectangular Coordinate Systems 

3. Lines 

4. Circles 

5. Equations and their Graphs 

6. Functions 

7. Limits 

86

Calculus 


CALCULUS 

By Eugene Don and Benay Don 

2001 / 226 pages 

ISBN: 9780071358972 


Considered to be the hardest mathematical problems to solve, word 

problems continue to terrify students across all math disciplines. 

 

problems once and for all by showing even the most math-phobic 

readers simple, step-by-step tips and techniques. How to Solve 

World Problems in Calculus reviews important concepts in calculus 

and provides solved problems and step-by-step solutions. Once 

students have mastered the basic approaches to solving calculus 

 

principles to even the most challenging advanced problems. Each 

 

theorems, and formulas. Topics range from vital pre-calculus review 

 

solutions and a 50-problem chapter are ideal for self-testing. Fully 

explained examples with step-by-step solutions. 


CALC I 

2nd Edition 


1998 / 150 pages 

ISBN: 9780070434080 


CONTENTS 

The Beginning--Limits. 

The Basics. 

Curve Sketching Made Easy. 

Word Problems Made Easy. 

Well, Less Difficult. 

Integral Applications. 

Odds and Ends. 

REVIEW COPY 










Single Variable Calculus 


NEW *9780073532325* 

CALCULUS 


4th Edition 



2012 (January 2011) / 1376 pages 

ISBN: 9780073532325 

ISBN: 9780071316569 [IE] 















CONTENTS 











a Curve 




















87

Calculus 












4.3, “Area” 






























































































CALCULUS, SINGLE VARIABLE: LATE 

TRANSCENDENTAL FUNCTIONS 

3rd Edition 

By Robert Smith, Millersville University and Roland Minton, Roanoke 

College 

2008 (January 2007) 

ISBN: 9780073314198 

ISBN: 9780071101981 [IE, without Mathzone] 


Students who have used Smith/Minton’s Calculus say it was easier 

to read than any other math book they’ve used. That testimony underscores 

the success of the authors’ approach which combines the 

most reliable aspects of mainstream Calculus teaching with the best 

elements of reform, resulting in a motivating, challenging book. Smith/ 

Minton wrote the book for the students who will use it, in a language 

that they understand, and with the expectation that their backgrounds 

may have some gaps. Smith/Minton provide exceptional, reality-based 

applications that appeal to students’ interests and demonstrate the 

 

Many new exercises and examples (for a total of 7,000 exercises 

and 1000 examples throughout the book) provide a careful balance 

 

exercises in every section that challenge students to make connec- 

 

Formulas”) that encourage students to think mathematically beyond 

 

“Today in Mathematics,” stress the contemporary dynamism of mathematical 

research and applications, connecting past contributions to 

 

 

sources: Within MathZone, instructors and students have access to 

a series of unique Conceptual Videos that help students understand 

 

88

Calculus 

Interactive Applets that help students master concepts and procedures 

and functions, 1600 algorithms , and 113 e-Professors. 

CONTENTS 


0.1 The Real Numbers and the Cartesian Plane 

0.2 Lines and Functions 

0.3 Graphing Calculators and Computer Algebra Systems 

0.4 Trigonometric Functions 

0.5 Transformations of Functions 


1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a 

Curve 

1.2 The Concept of Limit 

1.3 Computation of Limits 

1.4 Continuity and its Consequences / The Method of Bisections 

1.5 Limits Involving Infinity / Asysmptotes 

1.6 The Formal Definition of the Limit 

1.7 Limits and Loss-of-Significance Errors / Computer Representation 

or Real Numbers 

Chaper 2: Differentiation 

2.1 Tangent Lines and Velocity 

2.2 The Derivative / Alternative Derivative Notations / Numerical 

Differentiation 

2.3 Computation of Derivatives: The Power Rule / Higher Order 

Derivatives / Acceleration 

2.4 The Product and Quotient Rules 


2.6 Derivatives of the Trigonometric Functions 

2.7 Implicit Differentiation 

2.8 The Mean Value Theorem 

Chapter 3: Applications of Differentiation 

3.1 Linear Approximations and Newton’s Method 

3.2 Maximum and Minimum Values 

3.3 Increasing and Decreasing Functions 

3.4 Concavity and the Second Derivative Test 

3.5Overview of Curve Sketching 

3.6Optimization 

3.7 Related Rates 

3.8 Rates of Change in Economics and the Sciences 


4.1 Antiderivatives 

4.2 Sums and Sigma Notation / Principle of Mathematical Induction 

4.3 Area under a Curve 

4.4 The Definite Integral / Average Value of a Function 

4.5 The Fundamental Theorem of Calculus 


4.7 Numerical Integration / Error bounds for Numerical Integration 


5.1 Area Between Curves 

5.2 Volume: Slicing, Disks, and Washers 

5.3 Volumes by Cylindrical Shells 

5.4 Arc Length and Srface Area 

5.5 Projectile Motion 

5.6 Applications of Integration to Physics and Engineering 

Chapter 6: Exponentials, Logarithms and other Transcendental 

Functions 

6.1 The Natural Logarithm 


6.3 Exponentials 

6.4 The Inverse Trigonometric Functions 

6.5 The Calculus of the Inverse Trigonometric Functions 

6.6 The Hyperbolic Function 


7.1 Modeling with Differential Equations / Growth and Decay Problems 

/ Compound Interest 

7.2 Separable Differential Equations / Logistic Growth 

7.3 Direction Fields and Euler’s Method 

7.4 Systems of First-Order Differential Equations / Predator-Prey 

Systems 

7.6 Indeterminate Forms and L’Hopital’s Rule / Improper Integrals / 

A Comparison Test 



8.1 modeling with Differential Equations / Growth and Decay Problems 



8.3 Direction Fields and Euler’s Method / Systems of First Order 

Equations 


9.1 Sequences of Real Numbers 

9.2 Infinite Series 

9.3 The Integral Test and Comparison Tests 

9.4 Alternating Series / Estimating the Sum of an Alternating Series 

9.5 Absolute Convergence and the Ratio Test / The Root Test / Summary 

of Convergence Test 

9.6 Power Series 

9.7 Taylor Series / Representations of Functions as Series / Proof of 

Taylor’s Theorem 

9.8 Applications of Taylor Series / The Binomial Series 

9.9 Fourier Series 


10.1 Plane Curves and Parametric Equations 

10.2 Calculus and Parametric Equations 

10.3 Arc Length and Surface Area in Parametric Equations 

10.4 Polar Coordinates 

10.5 Calculus and Polar Coordinates 


10.7 Conic Sections in Polar Coordinates 


11.1 Vectors in the Plane 

11.2 Vectors in Space 

11.3 The Dot Product / Components and Projections 

11.4 The Cross Product 

11.5 Lines and Planes in Space 

11.6 Surfaces in Space 


12.1 Vector-Valued Functions 

12.2 The Calculus Vector-Valued Functions 

12.3 Motion in Space 

12.4 Curvature 

12.5 Tangent and Normal Vectors / Components of Acceleration, 

Kepler’s Laws 

12.6 Parametric Surfaces 



13.2 Limits and Continuity 


13.4 Tangent Planes and Linear Approximations / Increments and 

Differentials 

13.5 The Chain Rule / Implicit Differentiation 

13.6 The Gradient and Directional Derivatives 

13.7 Extrema of Functions of Several Variables 

13.8 Constrained Optimization and Lagrange Multipliers 



14.2 Area, Volume, and Center of Mass 

14.3 Double Integrals in Polar Coordinates 

14.4 Surface Area 

14.5 Triple Integrals / Mass and Center of Mass 

14.6 Cylindrical Coordinates 

14.7 Spherical Coordinates 

14.8 Change of Variables in Multiple Integrals 


15.1 Vector Fields 

15.2 Line Integrals 

15.3 Independence of Path and Conservative Vector Fields 

15.4 Green’s Theorem 

15.5 Curl and Divergence 

15.6 Surface Integrals 

15.7 The Divergence Theorem 

89

Calculus 

15.8 Stokes’ Theorem 

15.9 Applications of Vector Calculus 

Chapter 16: Second-Order Differential Equations 

16.1 Second-Order Equations with Constant Coefficients 

16.2 Nonhomogeneous Equations: Undetermined Coefficients 

16.3 Applications of Second-Order Differential Equations 

16.4 Power Series Solutions of Differential Equations 




CALCULUS: SINGLE VARIABLE 

Early Transcendental Functions 

3rd Edition 

By Robert T. Smith, Millersville University, and Roland B. Minton, 

Roanoke College 

2007 (December 2005) / Hardcover with access card 

ISBN: 9780073309439 

ISBN: 9780073215310 (with MathZone) - Out-of Print 

ISBN: 9780071107860 [IE with MathZone] 


CONTENTS 


0.1 Polynomials and Rational Functions 



0.4 Trigonometric and Inverse Trigonometric Functions 

0.5 Exponential and Logarithmic Functions. Hyperbolic Functions. 

Fitting a Curve to Data 



1.1 A First Look at Calculus 



1.4 Continuity and its Consequences. The Method of Bisections 

1.5 Limits Involving Infinity. Asymptotes. 

1.6 Formal Definition of the Limit. Exploring the Definition of Limit 

Graphically 

1.7 Limits and Loss-of-Significance Errors. Computer Representation 

of Real Numbers. 



2.2 The Derivative. Numerical Differentiation 

2.3 Computation of Derivatives: The Power Rule. Higher Order Derivatives. 

Acceleration. 




2.7 Derivatives of the Exponential and Logarithmic Functions 

2.8 Implicit Differentiation and Inverse Trigonometric Functions 


Chapter 3: Applications of Differentiation. 


3.2 Indeterminate Forms and L’Hopital’s Rule 




3.6 Overview of Curve Sketching 

3.7 Optimization 





4.2 Sums and Sigma Notation. Principle of Mathematical Induction 

4.3 Area 

4.4 The Definite Integral. Average Value of a Function 



4.7 Numerical Integration. Error Bounds for Numerical Integration 

4.8 The Natural Logarithm as an Integral. The Exponential Function 






5.4 Arc Length and Surface Area 


5.6 Applications of Integration to Economics and the Sciences 

5.7 Probability. 


6.1 Review of Formulas and Techniques 

6.2 Integration by Parts 

6.3 Trigonometric Techniques of Integration. Integrals Involving Powers 

of Trigonometric Functions. Trigonometric Substitution 

6.4 Integration of Rational Functions Using Partial Fractions. General 

Strategies for Integration Techniques 

6.5 Integration Tables and Computer Algebra Systems 

6.6 Improper Integrals. A Comparison Test. 

Chapter 7: First Order Differential Equations 

7.1 Growth and Decay Problems. Compound Interest. Modeling with 

Differential Equations. 

7.2 Separable Differential Equations. Logistic Growth. 


7.4 Systems of First Order Differential Equations. Predator-Prey 

Systems. 





8.4 Alternating Series. Estimating the Sum of an Alternating Series 

8.5 Absolute Convergence and the Ratio Test. The Root Test. Summary 

of Convergence Tests 


8.7 Taylor Series. Representations of Functions as Series. Proof of 


8.8 Applications of Taylor Series. The Binomial Series 













10.3 The Dot Product. Components and Projections 



10.6 Surfaces in Space. 



11.2 The Calculus of Vector-Valued Functions 



11.5 Tangent and Normal Vectors. Tangential and Normal. Components 

of Acceleration. Kepler’s Laws. 

11.6 Parametric Surfaces. 

Chapter 12: Functions of Several Variables and Differentiation. 


12.2 Limits and Continuity. 


12.4 Tangent Planes and Linear Approximations. Increments and 

Differentials. 

90

Calculus 




12.8 Constrained Optimization and Lagrange Multipliers. 






13.5 Triple Integrals. Mass and Center of Mass. 
















15.2 Non-homogeneous Equations: Undetermined Coefficients 

15.3 Applications of Second Order Equations 



Appendix B: Answers to Odd-Numbered Exercises. 

SCHAUM’S EASY OUTLINE OF CALCULUS 

2nd Edition 

By Elliott Mendenson, Queens College and Frank Ayres (deceased) 


ISBN: 9780071745826 


If you are looking for a quick nuts-and-bolts overview of calculus, it’s 


 

an emphasis on clarity and conciseness. 






fields 


Topics include: Functions, Sequences, Limits, and Continuity, Differentiation, 

Maxima and Minima, Differentiation of Special Functions, 

The Law of the Mean, Indeterminate Forms, Differentials, and Curve 

Sketching, Fundamental Integration Techniques and Applications, 

 

Differentiation Formulas for Common Mathematical Functions, Integration 

Formulas for Common Mathematical Functions 

Appendix B: Integration Formulas for Common Mathematical Functions; 

Index 


5th Edition 

By Frank Ayres (deceased) and Elliott Mendelson, Queens College 

2009 (July 2008) / 572 pages 

ISBN: 9780071508612 


A classic Schaum’s bestseller, thoroughly updated to meet the emphasis 

in current courses. The ideal review for the hundreds of thousands 

of colleges and high school students who enroll in calculus courses. 

CONTENTS 



3. Lines 

4. Circles 


6. Functions 

7. Limits 

8. Continuity 

























Substitutions 


34. Miscellaneous Substitutions 


36. Applications of Integration II: Area of a Surface of Revolution 


38. Curvature 

CONTENTS 

1. Functions, Sequences, Limits, and Continuity; 

2. Differentiation; 

3. Maxima and Minima; 

4. Differentiation of Special Functions; 

5. The Law of the Mean, Indeterminate Forms, Differentials, and 

Curve Sketching; 

6. Fundamental Integration Techniques and Applications; 

7. The Definite Integral, Plane Areas by Integration, Improper Integrals; 

Appendix A: Differentiation Formulas for Common Mathematical 

Functions; 

91

Calculus 

SCHAUM’S OUTLINE OF MATHEMATICA 

2nd Edition 

By Eugene Don 

2009 (April 2009) / Softcover 

ISBN: 9780071608282 


A classic Schaum’s Outline, thoroughly updated to match the latest 

course scope and sequence. The ideal review for the thousands of 

college students who enroll in courses that require the use of the 

Mathematica computer program. 

CONTENTS 

1. Getting Acquainted 

2. Basic Concepts 

3. Lists 

4. Two-Dimensional Graphics 

5. Three-Dimensional Graphics 

6. Equations 

7. Algebra and Trigonometry 

8. Differential Calculus 


10. Multivariate Calculus 

11. Ordinary Differential Equations 

12. Linear Algebra 


CALCULUS 



ISBN: 9780071635349 


This powerful problem-solver gives you 3,000 problems in calculus, 

fully solved step-by-step! From Schaum’s, the originator of the solvedproblem 

guide, and students’ favorite with over 30 million study guides 

sold this timesaver helps you master every type of calculus problem 

that you will face in your homework and on your tests, from inequalities 

to differential equations. Work the problems yourself, then check 

the answers, or go directly to the answers you need with a complete 

index. Compatible with any classroom text, Schaum’s 3000 Solved 

Problems in Calculus is so complete it’s the perfect tool for graduate 

or professional exam review! 


CALCULUS 

3rd Edition 


2009 (August 2009) / 400 pages 

ISBN: 9780071635356 


The guides that help students study faster, learn better- and get top 

 

latest course scope and sequences, with expanded explanations of 

 

Chapter 8: Limits 

Chapter 9: Special Limits 

Chapter 10: Continuity 

Chapter 11: The Slope of a Tangent Line 

Chapter 12: The Derivative 

Chapter 13: More on the Derivative 

Chapter 14: Maximum and Minimum Problems 

Chapter 15: The Chain Rule 

Chapter 16: Implicit Differentiation 

Chapter 17: The Mean-Value Theorem and the Sign of the Derivative 

Chapter 18: Rectilinear Motion and Instantaneous Velocity 

Chapter 19: Instantaneous Rate of Change 

Chapter 20: Related Rates 

Chapter 21: Approximation by Differentials; Newton’s Method 

Chapter 22: Higher-Order Derivatives 

Chapter 23: Applications of the Second Derivative and Graph Sketching 

Chapter 24: More Maximum and Minimum Problems 

Chapter 25: Angle Measure 

Chapter 26: Sine and Cosine Functions 

Chapter 27: Graphs and Derivatives of Sine and Cosine Functions 

Chapter 28: The Tangent and Other Trigonometric Functions 

Chapter 29: Antiderivatives 

Chapter 30: The Definite Integral 

Chapter 31: The Fundamental Theorem of Calculus 

Chapter 32: Applications of Integration I: Area and Arc Length 

Chapter 33: Applications of Integration II: Volume 

Chapter 34: The Natural Logarithm 

Chapter 35: Exponential Functions 

Chapter 36: L’Hopital’s Rule; Exponential Growth and Decay 

Chapter 37: Inverse Trigonometric Functions 

Chapter 38: Integration by Parts 

Chapter 39: Trigonometric Integrands and Trigonometric Substitutions 

Chapter 40: Integration of Rational Functions; The Method of Partial 

Fractions 

Appendix A: Trigonometric Formulas 

Appendix B: Basic Integration Formulas 

Appendix C: Geometric Formulas 

Appendix D: Trigonometric Functions 

Appendix E: Natural Logarithms 

Appendix F: Exponential Functions 

Answers to Supplementary Problems 

Index 


SCHAUM’S OUTLINE OF DIFFERENTIAL 

AND INTEGRAL CALCULUS, SI METRIC 

3rd Edition 

By Frank Ayres, Jr, Dickinson College 

1992 

ISBN: 9780071125314 [IE] 



CONTENTS 

Chapter 1: Coordinate Systems on a Line 

Chapter 2: Coordinate Systems in a Plane 

Chapter 3: Graphs of Equations 

Chapter 4: Straight Lines 

Chapter 5: Intersections of Graphs 

Chapter 6: Symmetry 

Chapter 7: Functions and Their Graphs 

92

Calculus 


Multi-Variable Calculus 


CALCULUS 


2001 / 226 pages 

ISBN: 9780071358972 




 






 


 


 




CALC I 

2nd Edition 


1998 / 150 pages 

ISBN: 9780070434080 


CONTENTS 

The Beginning--Limits. 

The Basics. 

Curve Sketching Made Easy. 

Word Problems Made Easy. 

Well, Less Difficult. 

Integral Applications. 

Odds and Ends. 




 





NEW *9780073532325* 

CALCULUS 


4th Edition 



2012 (January 2011) / 1376 pages 

ISBN: 9780073532325 

ISBN: 9780071316569 [IE] 















CONTENTS 











a Curve 




















93

Calculus 












4.3, “Area” 





























































































CALCULUS: MULTIVARIABLE 

Late Transcendental Functions, 3rd Edition 



2008 (January 2007) 

ISBN: 9780073314204 


Students who have used Smith/Minton’s Calculus say it was easier 

to read than any other math book they’ve used. That testimony underscores 

the success of the authors’ approach which combines the 

most reliable aspects of mainstream Calculus teaching with the best 

elements of reform, resulting in a motivating, challenging book. Smith/ 

Minton wrote the book for the students who will use it, in a language 

that they understand, and with the expectation that their backgrounds 

may have some gaps. Smith/Minton provide exceptional, reality-based 

applications that appeal to students’ interests and demonstrate the 

 

Many new exercises and examples (for a total of 7,000 exercises 

and 1000 examples throughout the book) provide a careful balance 

 

exercises in every section that challenge students to make connec- 

 

Formulas”) that encourage students to think mathematically beyond 

 

“Today in Mathematics,” stress the contemporary dynamism of mathematical 

research and applications, connecting past contributions to 

 

 

sources: Within MathZone, instructors and students have access to 

a series of unique Conceptual Videos that help students understand 

 

Interactive Applets that help students master concepts and procedures 

and functions, 1600 algorithms , and 113 e-Professors. 

94

Calculus 

CONTENTS 


0.1 The Real Numbers and the Cartesian Plane 

0.2 Lines and Functions 


0.4 Trigonometric Functions 



1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a 

Curve 



1.4 Continuity and its Consequences / The Method of Bisections 

1.5 Limits Involving Infinity / Asysmptotes 

1.6 The Formal Definition of the Limit 

1.7 Limits and Loss-of-Significance Errors / Computer Representation 

or Real Numbers 

Chaper 2: Differentiation 


2.2 The Derivative / Alternative Derivative Notations / Numerical 

Differentiation 

2.3 Computation of Derivatives: The Power Rule / Higher Order 

Derivatives / Acceleration 




2.7 Implicit Differentiation 








3.6Optimization 





4.2 Sums and Sigma Notation / Principle of Mathematical Induction 

4.3 Area under a Curve 

4.4 The Definite Integral / Average Value of a Function 



4.7 Numerical Integration / Error bounds for Numerical Integration 





5.4 Arc Length and Srface Area 


5.6 Applications of Integration to Physics and Engineering 

Chapter 6: Exponentials, Logarithms and other Transcendental 

Functions 

6.1 The Natural Logarithm 


6.3 Exponentials 

6.4 The Inverse Trigonometric Functions 

6.5 The Calculus of the Inverse Trigonometric Functions 

6.6 The Hyperbolic Function 


7.1 Modeling with Differential Equations / Growth and Decay Problems 




7.4 Systems of First-Order Differential Equations / Predator-Prey 

Systems 

7.6 Indeterminate Forms and L’Hopital’s Rule / Improper Integrals / 

A Comparison Test 



8.1 modeling with Differential Equations / Growth and Decay Problems 



8.3 Direction Fields and Euler’s Method / Systems of First Order 

Equations 





9.4 Alternating Series / Estimating the Sum of an Alternating Series 

9.5 Absolute Convergence and the Ratio Test / The Root Test / Summary 

of Convergence Test 


9.7 Taylor Series / Representations of Functions as Series / Proof of 


9.8 Applications of Taylor Series / The Binomial Series 













11.3 The Dot Product / Components and Projections 






12.2 The Calculus Vector-Valued Functions 



12.5 Tangent and Normal Vectors / Components of Acceleration, 

Kepler’s Laws 

12.6 Parametric Surfaces 





13.4 Tangent Planes and Linear Approximations / Increments and 

Differentials 

13.5 The Chain Rule / Implicit Differentiation 









14.5 Triple Integrals / Mass and Center of Mass 














Chapter 16: Second-Order Differential Equations 

95

Calculus 



16.3 Applications of Second-Order Differential Equations 





CALCULUS: MULTIVARIABLE: 

EARLY TRANSCENDENTAL FUNCTIONS 

3rd Edition 



2007 (February 2006) / Hardcover 

ISBN: 9780073309378 

ISBN: 9780073215327 (with MathZone) - Out-of-Print 

ISBN: 9780071107877 [IE with MathZone] - GOP 


CONTENTS 


0.1 Polynomials and Rational Functions 



0.4 Trigonometric and Inverse Trigonometric Functions 

0.5 Exponential and Logarithmic Functions. Hyperbolic Functions. 

Fitting a Curve to Data. 

0.6 Transformations of Functions. 


1.1 A First Look at Calculus 



1.4 Continuity and its Consequences. The Method of Bisections 

1.5 Limits Involving Infinity. Asymptotes. 

1.6 Formal Definition of the Limit. Exploring the Definition of Limit 

Graphically. 

1.7 Limits and Loss-of-Significance Errors. Computer Representation 

of Real Numbers. 


2.1 Tangent Lines and Velocity. 

2.2 The Derivative. Numerical Differentiation. 

2.3 Computation of Derivatives: The Power Rule. Higher Order Derivatives 

Acceleration 




2.7 Derivatives of the Exponential and Logarithmic Functions 

2.8 Implicit Differentiation and Inverse Trigonometric Functions 




3.2 Indeterminate Forms and L’Hopital’s Rule 





3.7 Optimization 


3.9 Rates of Change in Economics and the Sciences. 



4.2 Sums and Sigma Notation. Principle of Mathematical Induction. 

4.3 Area 

4.4 The Definite Integral. Average Value of a Function 



4.7 Numerical Integration. Error Bounds for Numerical Integration. 

4.8 The Natural Logarithm as an Integral. The Exponential Function 






5.4 Arc Length and Surface Area 


5.6 Applications of Integration to Economics and the Sciences. 



6.1 Review of Formulas and Techniques 

6.2 Integration by Parts 

6.3 Trigonometric Techniques of Integration. Integrals Involving Powers 

of Trigonometric Functions. Trigonometric Substitution 

6.4 Integration of Rational Functions Using Partial Fractions. General 

Strategies for Integration Techniques 

6.5 Integration Tables and Computer Algebra Systems 

6.6 Improper Integrals. A Comparison Test. 

Chapter 7: First Order Differential Equations 

7.1 Growth and Decay Problems. Compound Interest. Modeling with 


7.2 Separable Differential Equations. Logistic Growth. 


7.4 Systems of First Order Differential Equations. Predator-Prey 

Systems 





8.4 Alternating Series. Estimating the Sum of an Alternating Series 

8.5 Absolute Convergence and the Ratio Test. The Root Test. Summary 

of Convergence Tests 


8.7 Taylor Series. Representations of Functions as Series. Proof of 


8.8 Applications of Taylor Series. The Binomial Series 

8.9 Fourier Series. 








9.7 Conic Sections in Polar Coordinates. 




10.3 The Dot Product. Components and Projections. 






11.2 The Calculus of Vector-Valued Functions 



11.5 Tangent and Normal Vectors. Tangential and Normal Components 

of Acceleration. Kepler’s Laws 

11.6 Parametric Surfaces. 

Chapter 12: Functions of Several Variables and Differentiation 




12.4 Tangent Planes and Linear Approximations. Increments and 

Differentials 




96

Calculus 


Chapter 13: Multiple Integrals. 

13.1 Double Integrals. 

13.2 Area, Volume, and Center of Mass. 

13.3 Double Integrals in Polar Coordinates. 

13.4 Surface Area. 

13.5 Triple Integrals. Mass and Center of Mass. 

13.6 Cylindrical Coordinates. 


13.8 Change of Variables in Multiple Integrals. 










14.9 Applications of Vector Calculus. 




15.3 Applications of Second Order Equations 

15.4 Power Series Solutions of Differential Equations. 





5th Edition 

By Frank Ayres and Elliott Mendelson 

2009 (August 2008) / 552 pages 

ISBN: 9780071508612 


This review of standard college courses in calculus has been updated 

 

includes Green’s and Stokes’ theorems, as well as explanations of 

tough topics such as delta-epsilon proofs and Reimann Integrals. 

CONTENTS 



3. Lines 

4. Circles 


6. Functions 

7. Limits 

8. Continuity 

























Substitutions 


34. Techniques of Integration IV: Miscellaneous Substitutions 


36. Applications of Integration III: Area of a Surface of Revolution 


38. Curvature 

39. Plane Vectors 

40. Curvilinear Motion 

41. Polar Coordinates 

42. Infinite Sequences 


44. Series with Positive Terms. The Integral Test. Comparison Tests 

45. Alternating Series. Absolute and Conditional Convergence. The 

Ratio Test 

46. Power Series 

47. Taylor and Maclaurin Series. Taylor’s Formulas with Remainder 


49. Total Differential. Differentiability. Chain Rules 

50. Space Vectors 

51. Surfaces and Curves in Space 

52. Directional Derivatives. Maximum and Minimum Values. 

53. Vector Differentiation and Integration 

54. Double and Iterated Integrals 

55. Centroids and Moments of Inertia of Plane Areas 

56. Double Integration Applied to Volume under a Surface and the 

Area of a Curved Surface 

57. Triple Integrals 

58. Masses of Variable Density 

59. Differential Equations of First and Second Order 

SCHAUM’S OUTLINE OF MATHEMATICA 

2nd Edition 

By Eugene Don 

2009 (April 2009) / Softcover 

ISBN: 9780071608282 


A classic Schaum’s Outline, thoroughly updated to match the latest 

course scope and sequence. The ideal review for the thousands of 

college students who enroll in courses that require the use of the 

Mathematica computer program. 

CONTENTS 

1. Getting Acquainted 


3. Lists 

4. Two-Dimensional Graphics 

5. Three-Dimensional Graphics 

6. Equations 

7. Algebra and Trigonometry 

8. Differential Calculus 


10. Multivariate Calculus 

11. Ordinary Differential Equations 

12. Linear Algebra 

97

Calculus 

FIVE STEPS TO A 5 AP CALCULUS AB AND 

BC 

3rd Edition 

by William Ma 

2009 (November 2009) / Softcover 

ISBN: 9780071624756 


 

exam. 

The AP AB/BC Calculus exams have the largest enrollment of any 

AP exam. This fully revised edition covers the latest course syllabus 

 

sions of the exams. 



CALCULUS 


2001 / 226 pages 

ISBN: 9780071358972 

ISBN: 9780071203838 [IE] 


(International Edition is not for sale in Japan) 



 






 


 


 



REVIEW COPY 










98

Abstract Algebra ...............................................................................................127 

Advanced Calculus ...........................................................................................119 

Advanced Engineering Mathematics ................................................................115 

Advanced Geometry .........................................................................................121 

Combinatorics...................................................................................................114 

Complex Analysis .............................................................................................121 

Differential Equations .......................................................................................101 

Professional References ..............................................................................103 

Differential Equations with Boundary Value Problems .....................................104 


Functional Analysis ...........................................................................................124 

Graph Theory ...................................................................................................117 

History of Mathematics .....................................................................................119 

Introductory Analysis ........................................................................................118 

Linear Algebra .................................................................................................. 111 


Logic .................................................................................................................126 

Mathematical - References...............................................................................126 

Number Theory .................................................................................................120 

Numerical Analysis ...........................................................................................120 

Partial Differential Equations ............................................................................106 

Real Analysis ....................................................................................................125 

Topology ...........................................................................................................127 

Transition to Higher Math / Foundations of Higher Math ..................................110 

Professional References .............................................................................. 111 

Walter Rudin Student Series in Advanced Mathematics ..................................108 


99

New Titles 



Fourier Series and Boundary Value Problems, 8e Brown 9780078035975 106 



Elementary Number Theory, 7e Burton 9780073383149 120 

The History of Mathematics: An Introduction, 7e Burton 9780073383156 119 

100


Differential Equations 


DIFFERENTIAL EQUATIONS 

Theory, Technique, and Practice 

By George F. Simmons, Colorado College, and Steven G. Krantz, Washington 

University-St Louis 

2007 (December 2005) / 768 pages / Hardcover 


ISBN: 9780071254373 [IE] (GOP) 

www.mhhe.com/simmons 

CONTENTS 

Preface 

1 What is a Differential Equation? 

1.1 Introductory Remarks 

1.2 The Nature of Solutions 

1.3 Separable Equations 

1.4 First-Order Linear Equations 

1.5 Exact Equations 

1.6 Orthogonal Trajectories and Families of Curves 

1.7 Homogeneous Equations 

1.8 Integrating Factors 

1.9 Reduction of Order 

1.9.1 Dependent Variable Missing 

1.9.2 Independent Variable Missing 

1.10 The Hanging Chain and Pursuit Curves 

1.10.1 The Hanging Chain 

1.10.2 Pursuit Curves 

1.11 Electrical Circuits Anatomy of an Application: The Design of a 

Dialysis Machine. Problems for Review and Discovery. 

2 Second-Order Equations 

2.1 Second-Order Linear Equations with Constant Coefficients 

2.2 The Method of Undetermined Coefficients 

2.3 The Method of Variation of Parameters 

2.4 The Use of a Known Solution to Find Another 

2.5 Vibrations and Oscillations 

2.5.1 Undamped Simple Harmonic Motion 

2.5.2 Damped Vibrations 

2.5.3 Forced Vibrations 

2.5.4 A Few Remarks About Electricity 

2.6 Newton’s Law of Gravitation and Kepler’s Laws 

2.6.1 Kepler’s Second Law 

2.6.2 Kepler’s First Law 

2.6.3 Kepler’s Third Law 

2.7 Higher Order Equations. Anatomy of an Application: Bessel 

Functions and the Vibrating Membrane. Problems for Review and 

Discovery. 

3 Qualitative Properties and Theoretical Aspects 

3.0 Review of Linear Algebra 

3.0.1 Vector Spaces 

3.0.2 The Concept Linear Independence 

3.0.3 Bases 

3.0.4 Inner Product Spaces 

3.0.5 Linear Transformations and Matrices 

3.0.6 Eigenvalues and Eigenvectors 

3.1 A Bit of Theory 

3.2 Picard’s Existence and Uniqueness Theorem 

3.2.1 The Form of a Differential Equation 

3.2.2 Picard’s Iteration Technique 

3.2.3 Some Illustrative Examples 

3.2.4 Estimation of the Picard Iterates 

3.3 Oscillations and the Sturm Separation Theorem 

3.4 The Sturm Comparison Theorem. Anatomy of an Application: The 

Green’s Function. Problems for Review and Discovery. 

4 Power Series Solutions and Special Functions 

4.1 Introduction and Review of Power Series 

4.1.1 Review of Power Series. 

4.2 Series Solutions of First-Order Differential Equations. 

4.3 Second-Order Linear Equations: Ordinary Points. 

4.4 Regular Singular Points. 

4.5 More on Regular Singular Points. 

4.6 Gauss’s Hypergeometric Equation. Anatomy of an Application: 

Steady State Temperature in a Ball. Problems for Review and Discovery. 

5 Fourier Series: Basic Concepts. 

5.1 Fourier Coefficients. 

5.2 Some Remarks about Convergence. 

5.3 Even and Odd Functions: Cosine and Sine Series. 

5.4 Fourier Series on Arbitrary Intervals. 

5.5 Orthogonal Functions. Anatomy of an Application: Introduction to 

the Fourier Transform. Problems for Review and Discovery. 

6 Partial Differential Equations and Boundary Value Problems. 

6.1 Introduction and Historical Remarks. 

6.2 Eigenvalues, Eigenfunctions, and the Vibrating String. 

6.2.1 Boundary Value Problems. 

6.2.2 Derivation of the Wave Equation. 

6.2.3 Solution of the Wave Equation. 

6.3 The Heat Equation. 

6.4 The Dirichlet Problem for a Disc. 

6.4.1 The Poisson Integral 

6.5 Sturm-Liouville Problems. Anatomy of an Application: Some Ideas 

from Quantum Mechanics. Problems for Review and Discovery. 

7 Laplace Transforms. 

7.0 Introduction 

7.1 Applications to Differential Equations 

7.2 Derivatives and Integrals of Laplace Transforms 

7.3 Convolutions 

7.4 The Unit Step and Impulse Functions. Anatomy of an Application: 

Flow Initiated by an Impulsively-Started Flat Plate. Problems 

for Review and Discovery. 

8 The Calculus of Variations 

8.1 Introductory Remarks. 

8.2 Euler’s Equation. 

8.3 Isoperimetric Problems and the Like. 

8.3.1 Lagrange Multipliers 

8.3.2 Integral Side Conditions. 

8.3.3 Finite Side Conditions. Anatomy of an Application: Hamilton’s 

Principle and its Implications. Problems for Review and Discovery. 

9 Numerical Methods. 


9.2 The Method of Euler. 

9.3 The Error Term. 

9.4 An Improved Euler Method 

9.5 The Runge-Kutta Method. Anatomy of an Application: A Constant 

Perturbation Method for Linear, Second-Order Equations. 

Problems for Review and Discovery. 

10 Systems of First-Order Equations 


10.2 Linear Systems 

10.3 Homogeneous Linear Systems with Constant Coefficients 

10.4 Nonlinear Systems: Volterra’s Predator-Prey Equations. 

Anatomy of an Application: Solution of Systems with Matrices and 

Exponentials. Problems for Review and Discovery. 

11 The Nonlinear Theory. 

11.1 Some Motivating Examples 

11.2 Specializing Down 

11.3 Types of Critical Points: Stability 

11.4 Critical Points and Stability for Linear Systems 

11.5 Stability by Liapunov’s Direct Method 

11.6 Simple Critical Points of Nonlinear Systems 

11.7 Nonlinear Mechanics: Conservative Systems 

11.8 Periodic Solutions: The Poincaré-Bendixson Theorem. Anatomy 

of an Application: Mechanical Analysis of a Block on a Spring. Problems 


12 Dynamical Systems 

12.1 Flows 

12.1.1 Dynamical Systems 

101


12.1.2 Stable and Unstable Fixed Points 

12.1.3 Linear Dynamics in the Plane 

12.2 Some Ideas from Topology 

12.2.1 Open and Closed Sets 

12.2.2 The Idea of Connectedness 

12.2.3 Closed Curves in the Plane 

12.3 Planar Autonomous Systems 

12.3.1 Ingredients of the Proof of Poincaré-Bendixson. Anatomy 

of an Application: Lagrange’s Equations. Problems for Review and 

Discovery. Bibliography 


By Keng Cheng Ang 

2005 (October 2005) 

ISBN: 9780071250856 

(An Asian Publication) 

Many books on differential equations assume that the reader has a 

fairly sophisticated level of competence in calculus at the university 

level. Differential Equations: Models and Methods differs from them 

in that it enables a student with some basic knowledge of calculus to 

learn about differential equations and appreciate their applications. 

 

methods of solution and their use in mathematical models. Methods 

include analytic and graphical solutions, as well as numerical techniques. 

Readers will not only learn the necessary techniques of solving 

 

 

provide motivation for new concepts or techniques, and to illustrate 

the importance of differential equations. This book was written with 

student needs in mind; in particular, pre-university students taking 

 

them through the course. 

CONTENTS 

Preface 


2. Analytic Solutions 

3. Graphical Techniques 


5. Mathematical Models 

6. Further Applications 

Further Reading 

Appendix A: Table of Integrals 

Appendix B: Method of Least Squares 

Answers to Odd-numbered Problems 

Index 



A Modeling Approach 

By Glenn Ledder, University of Nebraska—Lincoln 

2005 / 768 pages 


ISBN: 9780071111515 [IE] 

www.mhhe.com/ledder 

CONTENTS 

1 Introduction: 

1.1 Natural Decay and Natural Growth. 

1.2 Differential Equations and Solutions. 

1.3 Mathematical Models and Mathematical Modeling. Case Study 1 

Scientific Detection of Art Forgery. 

2 Basic Concepts and Techniques: 

2.1 A Collection of Mathematical Models. 

2.2 Separable First-Order Equations. 

2.3 Slope Fields. 

2.4 Existence of Unique Solutions. 

2.5 Euler’s Method. 

2.6 Runge-Kutta Methods. Case Study 2 A Successful Volleyball 

Serve. 

3 Homogeneous Linear Equations. 

3.1 Linear Oscillators. 

3.2 Systems of Linear Algebraic Equations. 

3.3 Theory of Homogeneous Linear Equations. 

3.4 Homogeneous Equations with Constant Coefficients. 

3.5 Real Solutions from Complex Characteristic Values. 

3.6 Multiple Solutions for Repeated Characteristic Values. 

3.7 Some Other Homogeneous Linear Equations. Case Study 3 How 

Long Should Jellyfish Hold their Food? 

4 Nonhomogeneous Linear Equations: 

4.1 More on Linear Oscillator Models. 

4.2 General Solutions for Nonhomogeneous Equations. 

4.3 The Method of Undetermined Coefficients. 

4.4 Forced Linear Oscillators. 

4.5 Solving First-Order Linear Equations. 

4.6 Particular Solutions for Second-Order Equations by Variation of 

Parameters. Case Study 4 A Tuning Circuit for a Radio. 

5 Autonomous Equations and Systems: 

5.1 Population Models. 

5.2 The Phase Line. 

5.3 The Phase Plane. 

5.4 The Direction Field and Critical Points. 

5.5 Qualitative Analysis. Case Study 5 A Self-Limiting Population. 

6 Analytical Methods for Systems: 

6.1 Compartment Models. 

6.2 Eigenvalues and Eigenspaces. 

6.3 Linear Trajectories. 

6.4 Homogeneous Systems with Real Eigenvalues. 

6.5 Homogeneous Systems with Complex Eigenvalues. 

6.6 Additional Solutions for Deficient Matrices. 

6.7 Qualitative Behavior of Nonlinear Systems. Case Study 6 Invasion 

by Disease. 

7 The Laplace Transform: 

7.1 Piecewise-Continuous Functions. 

7.2 Definition and Properties of the Laplace Transform. 

7.3 Solution of Initial-Value Problems with the Laplace Transform. 

7.4 Piecewise-Continuous and Impulsive Forcing. 

7.5 Convolution and the Impulse Response Function. Case Study 7 

Growth of a Structured Population. 

8 Vibrating Strings: A Focused Introduction to Partial Differential 

Equations: 

8.1 Transverse Vibration of a String. 

8.2 The General Solution of the Wave Equation. 

8.3 Vibration Modes of a Finite String. 

8.4 Motion of a Plucked String. 

8.5 Fourier Series. Case Study 8 Stringed Instruments and Percussion. 

A Some Additional Topics: 

A.1 Using Integrating Factors to Solve First-Order Linear Equations 

(Chapter 2). 

A.2 Proof of the Existence and Uniqueness Theorem for First-Order 

Equations (Chapter 2). 

A.3 Error in Numerical Methods (Chapter 2). 

A.4 Power Series Solutions (Chapter 3). 

A.5 Matrix Functions (Chapter 6). 

A.6 Nonhomogeneous Linear Systems (Chapter 6). 

A.7 The One-Dimensional Heat Equation (Chapter 8). 

A.8 Laplace’s Equation (Chapter 8) 

102



DIFFERENTIAL EQUATIONS WITH 

APPLICATIONS AND HISTORICAL NOTES 

2nd Edition 

By George F. Simmons, Colorado College 

1991 / 640 pages 


ISBN: 9780071128070 [IE] 

CONTENTS 

1 The Nature of Differential Equations. 

2 First Order Equations. 

3 Second Order Linear Equations. 

4 Qualitative Properties of Solutions. 

5 Power Series Solutions and Special Functions. 

6 Fourier Series and Orthogonal Functions. 


8 Some Special Functions of Mathematical Physics. 


10 Systems of First Order Equations. 

11 Nonlinear Equations. 

12 The Calculus of Variations. 

13 The Existence and Uniqueness of Solutions. 




EQUATIONS 

3rd Edition 

By Richard Bronson, Fairleigh Dickinson University-Madison and 

Gabriel Costa, US Military Academy 

2009 (May 2009) / 384 pages 

ISBN: 9780071611626 


Thoroughly updated, this third edition of Schaum’s Outline of Differential 

Equations offers you new, faster techniques for solving differential 

equations generated by the emergence of high-speed computers. 

Differential equations, a linchpin of modern math, are essential in 

engineering, the natural sciences, economics, and business. Includes: 

• 563 fully solved problems 

• 800-plus supplementary problems 

• New chapter on modeling 

DIFFERENTIAL EQUATIONS DEMYSTIFIED 

By Steven Krantz, Washington University-St Louis 

2005 / 323 pages 

ISBN: 9780071440257 


CONTENTS 

Preface 

Chapter 1: What Is a Differential Equation? 

Chapter 2: Second-Order Equations 

Chapter 3: Power Series Solutions and Special Functions 

Chapter 4: Fourier Series: Basic Concepts 

Chapter 5: Partial Differential Equations and Boundary Value Problems 

Chapter 6: Laplace Transforms 

Chapter 7: Numerical Methods 

Chapter 8: Systems of First-Order Equations 

Final Exam 

Solutions to Exercises 

Bibliography 

Index 

SCHAUM’S OUTLINE OF LAPLACE 

TRANSFORMS 

By Murray Spiegel (deceased) 

1965 / 272 pages 

ISBN: 9780070602311 


CONTENTS 

The Laplace Transform. 

The Inverse Laplace Transform. 

Applications to Differential Equations. 

Applications to Integral and Difference Equations. 

Complex Variable Theory. 

Fourier Series and Integrals. 

The Complex Inversion Formula. 

Applications to Boundary-Value Problems. 

Appendix A: Table of General Properties of Laplace Transforms. 

Appendix B: Table of Special Laplace Transforms. 

Appendix C: Table of Special Functions. 




 




103


Differential Equations with 

Boundary Value Problems 



Theory, Technique, and Practice 

By George F. Simmons, Colorado College, and Steven G. Krantz, Washington 


2007 (December 2005) / 768 pages / Hardcover 


ISBN: 9780071254373 [IE] - GOP 

www.mhhe.com/simmons 

CONTENTS 

Preface 

1 What is a Differential Equation? 

1.1 Introductory Remarks 

1.2 The Nature of Solutions 

1.3 Separable Equations 

1.4 First-Order Linear Equations 

1.5 Exact Equations 

1.6 Orthogonal Trajectories and Families of Curves 

1.7 Homogeneous Equations 

1.8 Integrating Factors 

1.9 Reduction of Order 

1.9.1 Dependent Variable Missing 

1.9.2 Independent Variable Missing 

1.10 The Hanging Chain and Pursuit Curves 

1.10.1 The Hanging Chain 

1.10.2 Pursuit Curves 

1.11 Electrical Circuits Anatomy of an Application: The Design of a 

Dialysis Machine. Problems for Review and Discovery. 

2 Second-Order Equations 

2.1 Second-Order Linear Equations with Constant Coefficients 

2.2 The Method of Undetermined Coefficients 

2.3 The Method of Variation of Parameters 

2.4 The Use of a Known Solution to Find Another 

2.5 Vibrations and Oscillations 

2.5.1 Undamped Simple Harmonic Motion 

2.5.2 Damped Vibrations 

2.5.3 Forced Vibrations 

2.5.4 A Few Remarks About Electricity 

2.6 Newton’s Law of Gravitation and Kepler’s Laws 

2.6.1 Kepler’s Second Law 

2.6.2 Kepler’s First Law 

2.6.3 Kepler’s Third Law 

2.7 Higher Order Equations. Anatomy of an Application: Bessel 

Functions and the Vibrating Membrane. Problems for Review and 

Discovery. 

3 Qualitative Properties and Theoretical Aspects 

3.0 Review of Linear Algebra 

3.0.1 Vector Spaces 

3.0.2 The Concept Linear Independence 

3.0.3 Bases 

3.0.4 Inner Product Spaces 

3.0.5 Linear Transformations and Matrices 

3.0.6 Eigenvalues and Eigenvectors 

3.1 A Bit of Theory 

3.2 Picard’s Existence and Uniqueness Theorem 

3.2.1 The Form of a Differential Equation 

3.2.2 Picard’s Iteration Technique 

3.2.3 Some Illustrative Examples 

3.2.4 Estimation of the Picard Iterates 

3.3 Oscillations and the Sturm Separation Theorem 

3.4 The Sturm Comparison Theorem. Anatomy of an Application: The 

Green’s Function. Problems for Review and Discovery. 

4 Power Series Solutions and Special Functions 

4.1 Introduction and Review of Power Series 

4.1.1 Review of Power Series. 

4.2 Series Solutions of First-Order Differential Equations. 

4.3 Second-Order Linear Equations: Ordinary Points. 

4.4 Regular Singular Points. 

4.5 More on Regular Singular Points. 

4.6 Gauss’s Hypergeometric Equation. Anatomy of an Application: 

Steady State Temperature in a Ball. Problems for Review and Discovery. 

5 Fourier Series: Basic Concepts. 

5.1 Fourier Coefficients. 

5.2 Some Remarks about Convergence. 

5.3 Even and Odd Functions: Cosine and Sine Series. 

5.4 Fourier Series on Arbitrary Intervals. 

5.5 Orthogonal Functions. Anatomy of an Application: Introduction to 

the Fourier Transform. Problems for Review and Discovery. 


6.1 Introduction and Historical Remarks. 

6.2 Eigenvalues, Eigenfunctions, and the Vibrating String. 

6.2.1 Boundary Value Problems. 

6.2.2 Derivation of the Wave Equation. 

6.2.3 Solution of the Wave Equation. 

6.3 The Heat Equation. 

6.4 The Dirichlet Problem for a Disc. 

6.4.1 The Poisson Integral 

6.5 Sturm-Liouville Problems. Anatomy of an Application: Some Ideas 

from Quantum Mechanics. Problems for Review and Discovery. 


7.0 Introduction 

7.1 Applications to Differential Equations 

7.2 Derivatives and Integrals of Laplace Transforms 

7.3 Convolutions 

7.4 The Unit Step and Impulse Functions. Anatomy of an Application: 

Flow Initiated by an Impulsively-Started Flat Plate. Problems 


8 The Calculus of Variations 


8.2 Euler’s Equation. 

8.3 Isoperimetric Problems and the Like. 

8.3.1 Lagrange Multipliers 

8.3.2 Integral Side Conditions. 

8.3.3 Finite Side Conditions. Anatomy of an Application: Hamilton’s 

Principle and its Implications. Problems for Review and Discovery. 



9.2 The Method of Euler. 

9.3 The Error Term. 

9.4 An Improved Euler Method 

9.5 The Runge-Kutta Method. Anatomy of an Application: A Constant 

Perturbation Method for Linear, Second-Order Equations. 

Problems for Review and Discovery. 

10 Systems of First-Order Equations 


10.2 Linear Systems 

10.3 Homogeneous Linear Systems with Constant Coefficients 

10.4 Nonlinear Systems: Volterra’s Predator-Prey Equations. 

Anatomy of an Application: Solution of Systems with Matrices and 

Exponentials. Problems for Review and Discovery. 

11 The Nonlinear Theory. 

11.1 Some Motivating Examples 

11.2 Specializing Down 

11.3 Types of Critical Points: Stability 

11.4 Critical Points and Stability for Linear Systems 

11.5 Stability by Liapunov’s Direct Method 

11.6 Simple Critical Points of Nonlinear Systems 

11.7 Nonlinear Mechanics: Conservative Systems 

11.8 Periodic Solutions: The Poincaré-Bendixson Theorem. Anatomy 

of an Application: Mechanical Analysis of a Block on a Spring. Problems 


104


12 Dynamical Systems 

12.1 Flows 

12.1.1 Dynamical Systems 

12.1.2 Stable and Unstable Fixed Points 

12.1.3 Linear Dynamics in the Plane 

12.2 Some Ideas from Topology 

12.2.1 Open and Closed Sets 

12.2.2 The Idea of Connectedness 

12.2.3 Closed Curves in the Plane 

12.3 Planar Autonomous Systems 

12.3.1 Ingredients of the Proof of Poincaré-Bendixson. Anatomy 

of an Application: Lagrange’s Equations. Problems for Review and 

Discovery. Bibliography 

SCHAUM’S EASY OUTLINE OF 


By Richard Bronson, Fairleigh Dickinson University-Madison 

2003 / 144 pages 

ISBN: 9780071409674 



For students looking for a quick nuts-and-bolts overview, it would 

have to be Schaum’s Easy Outline series. Every book in this series 

 

predecessor. With an emphasis on clarity and brevity, each new title 

features a streamlined and updated format and the absolute essence 

of the subject, presented in a concise and readily understandable 

form. Graphic elements such as sidebars, reader-alert icons, and 

boxed highlights feature selected points from the text, illuminate 

keys to learning, and give students quick pointers to the essentials. 



EQUATIONS 

3rd Edition 

By Richard Bronson, Fairleigh Dickinson University-Madison and 

Gabriel Costa, US Military Academy 

2009 (May 2009) / 384 pages 

ISBN: 9780071611626 


Thoroughly updated, this third edition of Schaum’s Outline of Differential 

Equations offers you new, faster techniques for solving differential 

equations generated by the emergence of high-speed computers. 

Differential equations, a linchpin of modern math, are essential in 

engineering, the natural sciences, economics, and business. Includes: 

• 563 fully solved problems 

• 800-plus supplementary problems 

• New chapter on modeling 


TRANSFORMS 


1965 / 272 pages 

ISBN: 9780070602311 


CONTENTS 












DIFFERENTIAL EQUATIONS DEMYSTIFIED 

By Steven Krantz, Washington University-St Louis 

2005 / 323 pages 

ISBN: 9780071440257 


CONTENTS 

Preface 

Chapter 1: What Is a Differential Equation? 

Chapter 2: Second-Order Equations 

Chapter 3: Power Series Solutions and Special Functions 

Chapter 4: Fourier Series: Basic Concepts 

Chapter 5: Partial Differential Equations and Boundary Value Problems 

Chapter 6: Laplace Transforms 

Chapter 7: Numerical Methods 

Chapter 8: Systems of First-Order Equations 

Final Exam 

Solutions to Exercises 

Bibliography 

Index 

REVIEW COPY 










105


Partial Differential Equations 


NEW *9780078035975* 

FOURIER SERIES AND 

BOUNDARY VALUE 

PROBLEMS 

8th Edition 

By James Ward Brown, University of Michigan- 

Dearborn and Ruel V Churchill (deceased) 


ISBN: 9780078035975 

ISBN: 9780071086158 [IE] 

www.mhhe.com/BrownFourier 

 

is an introduction to Fourier series and their applications to boundary 

value problems in partial differential equations of engineering and 

physics. It will primarily be used by students with a background in 

ordinary differential equations and advanced calculus. There are two 

 

orthogonal sets of functions and representations of arbitrary functions 

in series of functions from such sets. The second is a clear presentation 

of the classical method of separation of variables used in solving 

boundary value problems with the aid of those representations. 

FEATURES 

Primary Focus: The text’s primary focus is to find solutions to 

specific problems, rather than developing general theories. 

CONTENTS 

Preface 

1 Fourier Series 

Piecewise Continuous Functions 

Fourier Cosine Series 

Examples 

Fourier Sine Series 

Examples 

Fourier Series 

Examples 

Adaptations to Other Intervals 

2 Convergence of Fourier Series 

One-Sided Derivatives 

A Property of Fourier Coefficients 

Two Lemmas 

A Fourier Theorem 

Discussion of the Theorem and Its Corollary 

Convergence on Other Intervals 

A Lemma 

Absolute and Uniform Convergence of Fourier Series 

Differentiation of Fourier Series 

Integration of Fourier Series 

3 Partial Differential Equations of Physics 

Linear Boundary Value Problems 

One-Dimensional Heat Equation 

Related Equations 

Laplacian in Cylindrical and Spherical Coordinates 

Derivations 

Boundary Conditions 

A Vibrating String 

Vibrations of Bars and Membranes 

General Solution of the Wave Equation 

Types of Equations and Boundary Equations 

4 The Fourier Method 

Linear Operators 

Principle of Superposition 

A Temperature Problem 

A Vibrating String Problem 

Historical Development 

5 Boundary Value Problems 

A Slab with Faces at Prescribed Temperatures 

Related Problems 

A Slab with Internally Generated Heat 

Steady Temperatures in a Rectangular Plate 

Cylindrical Coordinates 

A String with Prescribed Initial Conditions 

Resonance 

An Elastic Bar 

Double Fourier Series 

Periodic Boundary Conditions 

6 Fourier Integrals and Applications 

The Fourier Integral Formula 

Dirichlet’s Integral 

Two Lemmas 

A Fourier Integral Theorem 

The Cosine and Sine Integrals 

More on Superposition of Solutions 

Temperatures in a Semi-Infinite Solid 

Temperatures in an Unlimited Medium 

7 Orthonormal Sets 

Inner Products and Orthonormal Sets 

Examples 

Generalized Fourier Series 

Examples 

Best Approximation in the Mean 

Bessel’s Inequality and Parseval’s Equation 

Applications to Fourier Series 

8 Sturm-Liouville Problems and Applications 

Regular Sturm-Liouville Problems 

Modifications 

Orthogonality of Eigenfunctions 

Real-Valued Eigenfunctions and Nonnegative Eigenvalues 

Methods of Solution 

Examples of Eigenfunction Expansions 

A Temperature Problem in Rectangular Coordinates 

Another Problem 

Other Coordinates 

A Modification of the Method 

Another Modification 

A Vertically Hung Elastic Bar 

9 Bessel Functions and Applications 

Bessel Functions Jn(x) 

General Solutions of Bessel’s Equation 

Recurrence Relations 

Bessel’s Integral Form 

Some Consequences of the Integral Forms 

The Zeros of Jn(x) 

Zeros of Related Functions 

Orthogonal Sets of Bessel Functions 

Proof of the Theorems 

The Orthonormal Functions 

Fourier-Bessel Series 

Examples 

Temperatures in a Long Cylinder 

Internally Generated Heat 

Vibration of a Circular Membrane 

10 Legendre Polynomials and Applications 

Solutions of Legendre’s Equation 

Legendre Polynomials 

Orthogonality of Legendre Polynomials 

Rodrigues’ Formula and Norms 

Legendre Series 

106


The Eigenfunctions Pn(cos ¿) 

Dirichlet Problems in Spherical Regions 

Steady Temperatures in a Hemisphere 

11 Verification of Solutions and Uniqueness 

Abel’s Test for Uniform Convergence 

Verification of Solution of Temperature Problem 

Uniqueness of Solutions of the Heat Equation 

Verification of Solution of Vibrating String Problem 

Uniqueness of Solutions of the Wave Equation 

Appendixes 

Bibliography 

Some Fourier Series Expansions 

Solutions of Some Regular Sturm-Liouville Problems 

Index 


FOURIER SERIES AND BOUNDARY VALUE 

PROBLEMS 

7th Edition 

By James Ward Brown, University of Michigan-Dearborn and Ruel 

Churchill (deceased) 

2008 (August 2006) / 384 pages 

ISBN: 9780073051932 

ISBN: 9780071259170 [IE] 

 

is an introduction to Fourier series and their applications to boundary 

value problems in partial differential equations of engineering and 

physics. It will primarily be used by students with a background in 

ordinary differential equations and advanced calculus. There are two 

 

orthogonal sets of functions and representations of arbitrary functions 

in series of functions from such sets. The second is a clear presentation 

of the classical method of separation of variables used in solving 

boundary value problems with the aid of those representations. 

CONTENTS 

Preface 

1 Fourier Series 

2 Convergence of Fourier Series 

3 Partial Differential Equations of Physics 

4 The Fourier Method 


6 Fourier Integrals and Applications 

7 Orthonormal Sets 

8 Sturm-Liouville Problems and Applications 

9 Bessel Functions and Applications 

10 Legendre Polynomials and Applications 

11 Verification of Solutions and Uniqueness 

Appendixes 

Bibliography 

Some Fourier Series Expansions 

Solutions of Some Regular Sturm-Liouville Problems 

Index 

SCHAUM’S OUTLINE OF PARTIAL 


By Paul DuChateau, Colorado State University and D W Zachmann, 

Colorado State University 

2011 (January 2011) / 272 pages 

ISBN: 9780071756181 


Schaum’s Outline of Partial Differential Equations is a clear, readily 

understood review of the standard college course in partial differential 

equations. This powerful study tool takes students step-by-step 

through the subject and gives them 290 accompanying related 

problems with fully worked solutions. Students get plenty of practice 

problems to do on their own, working at their own speed. 

CONTENTS 

1. Introduction 

2. Classification and Characteristics 

3. Qualitative Behavior of Solutions to Elliptic Equations 

4. Qualitative Behavior of Solutions to Evolution Equations 

5. First-Order Equations 

6. Eigenfunction Expansions and Integral Transforms: Theory 

7. Eigenfunction Expansions and Integral Transforms: Applications 

8. Green’s Functions 

9. Difference Methods for Parabolic Equations 

10. Difference and Characteristic Methods for Parabolic Equations 

11. Difference Methods for Hyperbolic Equations 

12. Difference Methods for Elliptic Equations 

13. Variational Formulation of Boundary Value Problems 

14. The Finite Element Method: An Introduction 

SCHAUM’S OUTLINE OF FOURIER 

ANLAYSIS WITH APPLICATIONS TO 

BOUNDARY VALUE PROBLEMS 

By Murray Spiegel 

1974 / 208 pages 

ISBN: 9780070602199 


CONTENTS 

Boundary Value Problems 

Fourier Series and Applications 

Orthogonal Functions 

Gamma, Beta and Other Special Functions 

Fourier Integrals and Applications 

Bessel Functions and Applications 

Legendre Functions and Applications 

Hermite, Laguerre and Other Orthogonal Functions 

Appendices A: Uniqueness of Solutions 

Appendices B: Special Fourier Series 

Appendices C: Special Fourier Transforms 

Appendices D: Tables of Values for J0(x) and J1(x) 

Appendices E: Zeros of Bessel Functions 


TRANSFORMS 


1965 / 272 pages 

ISBN: 9780070602311 


CONTENTS 












107


Walter Rudin Student Series 

in Advanced Mathematics 


INTRODUCTION TO ENUMERATIVE 

COMBINATORICS 

By Miklos Bona, University of Florida at Gainesville 

2007 / 544 pages 

ISBN: 9780073125619 

ISBN: 9780071254151 [IE] 

CONTENTS 

Foreword 

Preface 


I How: Methods 

1 Basic Methods 

2 Direct Applications of Basic Methods 

3 Generating Functions 

II What: Topics 

4 Counting Permutations 

5 Counting Graphs 

6 Extremal Combinatorics 

III What Else: Special Topics 

7 Symmetric Structures 

8 Sequences in Combinatorics 

9 Counting Magic Squares and Magic Cubes 

A The Method of Mathematical Induction 

A.1 Weak Induction 

A.2 Strong Induction 

Bibliography 

Index 

Frequently Used Notation 


TRANSITION TO HIGHER MATHEMATICS 

Structure and Proof 

By Bob Dumas, University of Washington and John McCarthy, Washington 


2007 / 304 pages 

ISBN: 9780073533537 

ISBN: 9780071106474 [IE] 

CONTENTS 

Chapter 0. Introduction 

0.1. Why this book is 

0.2. What this book is 

0.3. What this book is not 

0.4. Advice to the Student 

0.5. Advice to the Instructor 

0.6. Acknowledgements 

Chapter 1. Preliminaries 

1.1. “And” “Or” 

1.2. Sets 

1.3. Functions 

1.4. Injections, Surjections, Bijections 

1.5. Images and Inverses 

1.6. Sequences 

1.7. Russell’s Paradox 

1.8. Exercises 

1.9. Hints to Get Started on Some Exercises 

Chapter 2. Relations 

2.1. Definitions 

2.2. Orderings 

2.3. Equivalence Relations 

2.4. Constructing Bijections 

2.5. Modular Arithmetic 


Chapter 3. Proofs 

3.1. Mathematics and Proofs 

3.2. Propositional Logic 

3.3. Formulas 

3.4. Quantifiers 

3.5. Proof Strategies 


Chapter 4. Principle of Induction 

4.1. Well-Orderings 

4.2. Principle of Induction 

4.3. Polynomials 

4.4. Arithmetic-Geometric Inequality 


Chapter 5. Limits 

5.1. Limits 

5.2. Continuity 

5.3. Sequences of Functions 


Chapter 6. Cardinality 

6.1. Cardinality 

6.2. Infinite Sets 

6.3. Uncountable Sets 

6.4. Countable Sets 

6.5. Functions and Computability 


Chapter 7. Divisibility 

7.1. Fundamental Theorem of Arithmetic 

7.2. The Division Algorithm 

7.3. Euclidean Algorithm 

7.4. Fermat’s Little Theorem 

7.5. Divisibility and Polynomials 


Chapter 8. The Real Numbers 

8.1. The Natural Numbers 

8.2. The Integers 

8.3. The Rational Numbers 

8.4. The Real Numbers 

8.5. The Least Upper Bound Principle 

8.6. Real Sequences 

8.7. Ratio Test 

8.8. Real Functions 

8.9. Cardinality of the Real Numbers 

8.10. Order-Completeness 


Chapter 9. Complex Numbers 

9.1. Cubics 

9.2. Complex Numbers 

9.3. Tartaglia-Cardano Revisited 

9.4. Fundamental Theorem of Algebra 

9.5. Application to Real Polynomials 

9.6. Further Remarks 


Appendix A. The Greek Alphabet 

Appendix B. Axioms of Zermelo-Fraenkel with the Axiom of Choice 

Bibliography 

Index 

108



INTRODUCTION TO GRAPH THEORY 

By Gary Chartrand, Western Michigan University—Kalamazoo and Ping 

Zhang, Western Michigan University—Kalamazoo 

2005 (May 2004) / 464 pages 


ISBN: 9780071238229 [IE] 

CONTENTS 

1. Introduction: Graphs and Graph Models. Connected Graphs. 

Common Classes of Graphs. 

2. Degrees: The Degree of a Vertex. Regular Graphs. Degree 

Sequences. Excursion: Graphs and Matrices. Exploration: Irregular 

Graphs. 

3. Isomorphic Graphs: The Definition of Isomorphisms. Isomorphism 

as a Relation. Excursion: Recognition, Reconstruction, Solvability. 

Excursion: Graphs and Groups. 

4. Trees: Bridges. Trees. The Minimum Spanning Tree Problem. 

Excursion: The Number of Spanning Trees. Exploration: Comparing 

Trees. 

5. Connectivity: Cut-Vertices. Blocks. Connectivity. Menger’s Theorem. 

Exploration: Geodetic Sets. 

6. Traversability: Eulerian Graphs. Hamiltonian Graphs. Exploration: 

Hamiltonian Walks and Numbers. Excursion: The Early Books 

of Graph Theory. 

7. Digraphs: Strong Digraphs. Tournaments. Excursion: How to Make 

Decisions. Exploration: Wine Bottle Problems. 

8. Matchings and Factorization: Matchings. Factorizations. Decompositions 

and Graceful Labelings. Excursion: Instant Insanity. 

Excursion: The Petersen Graph. Exploration: -Labeling of Graphs. 

9. Planarity: Planar Graphs. Embedding Graphs on Surfaces. Excursion: 

Graphs Minors. Exploration: Embedding Graphs in Graphs. 

10. Coloring Graphs: The Four Color Problem. Vertex Coloring. 

Edge Coloring. Excursion: The Heawood Map-Coloring Theorem. 

Exploration: Local Coloring. 

11. Ramsey Numbers: The Ramsey Number of Graphs. Turan’s 

Theorem. Exploration: Rainbow Ramsey Numbers. Excursion: 

Erd?umbers. 

12. Distance: The Center of a Graph. Distant Vertices. Excursion: 

Locating Numbers. Excursion: Detour Distance and Directed Distance. 

Exploration: The Channel Assignment Problem. Exploration: Distance 

Between Graphs. 

13. Domination: The Domination Number of a Graph. Exploration: 

Stratification. Exploration: Lights Out. Excursion: And Still It Grows 

More Colorful. 

Appendix 1. Sets and Logic. 

Appendix 2. Equivalence Relations and Functions. 

Appendix 3. Methods of Proof. 

Answers and Hints to Odd-Numbered Exercises. 

References. 

Index of Symbols. 

Index of Mathematical Terms 


REAL AND COMPLEX ANALYSIS 

3rd Edition 

By Walter Rudin, University of Wisconsin-Wauwatosa 

1987 / 430 pages 

ISBN: 9780070542341 

ISBN: 9780071002769 [IE] 

CONTENTS 

Preface 

Prologue: The Exponential Function 

Chapter 1: Abstract Integration 

Chapter 2: Positive Borel Measures 

Chapter 3: Lp-Spaces 

Chapter 4: Elementary Hilbert Space Theory 

Chapter 5: Examples of Banach Space Techniques 

Chapter 6: Complex Measures 


Chapter 8: Integration on Product Spaces 

Chapter 9: Fourier Transforms 

Chapter 10: Elementary Properties of Holomorphic Functions 

Chapter 11: Harmonic Functions 

Chapter 12: The Maximum Modulus Principle 

Chapter 13: Approximation by Rational Functions 

Chapter 14: Conformal Mapping 

Chapter 15: Zeros of Holomorphic Functions 

Chapter 16: Analytic Continuation 

Chapter 17: Hp-Spaces 

Chapter 18: Elementary Theory of Banach Algebras 

Chapter 19: Holomorphic Fourier Transforms 

Chapter 20: Uniform Approximation by Polynomials 

Appendix: Hausdorff’s Maximality Theorem 

Notes and Comments 

Bibliography 

List of Special Symbols 

Index 

109



PRINCIPLES OF MATHEMATICAL ANALYSIS 

3rd Edition 

By Walter Rudin, University of Wisconsin-Wauwatosa 

1976 / 352 pages 

ISBN: 9780070542358 

ISBN: 9780070856134 [IE] 

CONTENTS 

Chapter 1: The Real and Complex Number Systems 

Chapter 2: Basic Topology 

Chapter 3: Numerical Sequences and Series 

Chapter 4: Continuity 


Chapter 6: The Riemann-Stieltjes Integral 

Chapter 7: Sequences and Series of Functions 

Chapter 8: Some Special Functions 

Chapter 9: Functions of Several Variables 

Chapter 10: Integration of Differential Forms 

Chapter 11: The Lebesgue Theory 

Exercises 

Bibliography 


Index 

Transition to Higher Math / 

Foundations of Higher Math 


TRANSITION TO HIGHER MATHEMATICS 

Structure and Proof 

By Bob A. Dumas, University Of Washington, and John E. McCarthy, 

Washington University-St Louis 

2007 (February 2006) / 416 pages / Hardcover 

ISBN: 9780073533537 

ISBN: 9780071106474 [IE] 

CONTENTS 

Chapter 0. Introduction. 

0.1. Why this book is 

0.2. What this book is 

0.3. What this book is not 

0.4. Advice to the Student 

0.5. Advice to the Teacher 

0.6. Acknowledgements 

Chapter 1. Preliminaries 

1.1. “And” “Or” 

1.2. Sets 

1.3. Functions 

1.4. Injections, Surjections, Bijections 

1.5. Images and Inverses 

1.6. Sequences 

1.7. Russell’s Paradox 


Chapter 2. Relations 

2.1. Definitions 

2.2. Orderings 

2.3. Equivalence Relations 

2.4. Constructing Bijections 

2.5. Modular Arithmetic 


Chapter 3. Proofs 

3.1. Mathematics and Proofs 

3.2. Propositional Logic 

3.3. Formulas 

3.4. Quantifiers 

3.5. Proof Strategies 

3.6. Exercises. 

Chapter 4. Principle of Induction 

4.1. Well-orderings 

4.2. Principle of Induction 

4.3. Polynomials 

4.4. Arithmetic-Geometric Inequality 


Chapter 5. Limits 

5.1. Limits 

5.2. Continuity 

5.3. Sequences of Functions 


Chapter 6. Cardinality 

6.1. Cardinality 

6.2. Infinite Sets 

6.3. Uncountable Sets 

6.4. Countable Sets 

6.5. Functions and Computability 

6.6. Exercises. 

Chapter 7. Divisibility 

7.1. Fundamental Theorem of Arithmetic 

7.2. The Division Algorithm 

7.3. Euclidean Algorithm 

7.4. Fermat’s Little Theorem 

7.5. Divisibility and Polynomials 


Chapter 8. The Real Numbers. 

8.1. The Natural Numbers 

8.2. The Integers 

8.3. The Rational Numbers 

8.4. The Real Numbers 

8.5. The Least Upper Bound Principle 

8.6. Real Sequences 

8.7. Ratio Test 

8.8. Real Functions 

8.9. Cardinality of the Real Numbers 


Chapter 9. Complex Numbers 

9.1. Cubics 

9.2. Complex Numbers 

9.3. Tartaglia-Cardano Revisited 

9.4. Fundamental Theorem of Algebra 

9.5. Application to Real Polynomials 

9.6. Further remarks 


Appendix A. The Greek Alphabet 

Appendix B. Axioms of Zermelo-Fraenkel with the Axiom of Choice 

Appendix C. Hints to get started on early exercises. 

Bibliography. 

Index 

110



MATH PROOFS DEMYSTIFIED 


2005 / 290 pages 

ISBN: 9780071445764 


CONTENTS 

Part One: The Rules of Reason 

Chapter 1: The Basics of Propositional Logic 

Chapter 2: How Sentences are Put Together 

Chapter 3: Formalities and Techniques 

Chapter 4: Vagaries of Logic 


Part Two: Proofs in Action 

Chapter 5: Some Theoretical Geometry 

Chapter 6: Sets and Numbers 

Chapter 7: A Few Historic Tidbits 


Final Rxam 

Answers to Quiz, Test and Exam Questions 


Index 

Linear Algebra 


INTRODUCTION TO LINEAR ALGEBRA 

James DeFranza, St. Lawrence-Lewis Boces, Daniel Gagliardi and Suny 

Canton 


ISBN: 9780073532356 

ISBN: 9780071270540 [IE] 

www.mhhe.com/defranza 

Linear Algebra with Applications is an introductory text targeted to 

 

mathematics. The organization of this text is motivated by the authors’ 

experience which tells them what essential concepts should be mastered 

by students in a one semester undergraduate Linear Algebra 

course. The authors’ main objectives are to fully develop each topic 

before moving on and to connect topics naturally. The authors take 

great care to meet both these objectives, because this organization 

will allow instructors teaching from this text to stay on task so that 

each topic can be covered with the depth required before progressing 

to the next logical one. As a result the reader is prepared for each 

new unit and there is no need to repeat a concept in a subsequent 

chapter when it is utilized. This text is geared towards an introductory 

 

students. However, it offers the opportunity to introduce the importance 

of abstraction, not only in mathematics, but in many other areas 

where Linear Algebra is used. The textbook’s approach is to take 

advantage of this opportunity by presenting abstract vector spaces 

as early as possible. Throughout the text, the authors are mindful of 

 

 

 

subtle concept of linear independence, the authors use addition and 

scalar multiplication of vectors in Euclidean Space. The authors have 

strived to create a balance between computation, problem solving, 

and abstraction. This approach equips students with the necessary 

skills and problem solving strategies in an abstract setting that allows 

for a greater understanding and appreciation for the numerous applications 

of the subject. 

CONTENTS 

Introduction to Linear Algebra, Defranza & Gigliardi 

Chapter 1 Systems of Linear Equations and Matrices 1 

--1.1 Systems of Linear Equations 

Exercise Set 1.1 

--1.2 Matrices and Elementary Row Operations 


--1.3 Matrix Algebra 


--1.4 The Inverse of a Square Matrix 


--1.5 Matrix Equations 


--1.6 Determinants 


--1.7 Elementary Matrices and LU Factorization 


--1.8 Applications of Systems of Linear Equatio 


Review Exercises 

Chapter Test 

Chapter 2 Linear Combinations and Linear Independence 

--2.1 Vectors in Rn 


--2.2 Linear Combinations 


--2.3 Linear Independence 



Chapter Test 

Chapter 3 Vector Spaces 

--3.1 Definition of a Vector Space 


--3.2 Subspaces 


--3.3 Basis and Dimension 


--3.4 Coordinates and Change of Basis 


--3.5 Application : Differential Equations 



Chapter Test 

Chapter 4 Linear Transformations 

--4.1 Linear Transformations 


--4.2 The Null Space and Range 


--4.3 Isomorphisms 


--4.4 Matrix Representation of a Linear Transformation 


--4.5 Similarity 


--4.6 Application : Computer Graphics 



Chapter Test 

Chapter 5 Eigenvalues and Eigenvectors 

--5.1 Eigenvalues and Eigenvectors 


--5.2 Diagonalization 


--5.3 Application : Systems of Linear Different 

111



--5.4 Application : Markov Chains 



Chapter Test 

Chapter 6 Inner Product Spaces 

--6.1 The Dot Product on Rn 


--6.2 Inner Product Spaces 


--6.3 Orthonormal Bases 


--6.4 Orthogonal Complements 


--6.5 Application : Least Squares Approximation 


--6.6 Diagonalization of Symmetric Matrices 


--6.7 Application : Quadratic Forms 


--6.8 Application : Singular Value Decomposition 



Chapter Test 

A Preliminaries 

A.1 Algebra of Sets 

Exercise Set A.1 

A.2 Functions 


A.3 Techniques of Proof 


A.4 Mathematical Induction 


Answers to Odd-Numbered Exercises 

A.3 Techniques of Proof 


A.4 Mathematical Induction 


Answers to Odd-Numbered Exercises 


LINEAR ALGEBRA WITH APPLICATIONS 

6th Edition 

by Keith Nicholson, University of Calgary 


ISBN: 9780070985100 

ISBN: 9780071088374 [IE] 

(McGraw-Hill Canada Title) 

www.mcgraw-hill.ca/college/nicholson 

Nicholson Linear Algebra 6e introduces the general idea of Linear 

Algebra much earlier than the competition keeping with the same 

rigorous and concise approach to linear algebra. Along with the many 

diagrams and examples that help students visualize, the 6e also 

keeps with the continuous introduction of concepts. #1 advantage is 

in Chap 5 known as the “bridging chapter” helps stop students from 

“hitting the wall” when abstract vector spaces are introduced in chap 6. 

CONTENTS 


Chapter 2: Matrix Algebra 

Chapter 3: Determinants and Diagonalization 

Chapter 4: Vector Geometry 

Chapter 5: The Vector Space Rn 

Chapter 6: Vector Spaces 

Chapter 7: Linear Transformations 

Chapter 8: Orthogonality 

Chapter 9: Change of Basis 

Chapter 10: Inner Product Spaces 

Chapter 11:Canonical Forms 

Appendix A: Complex Numbers 

Appendix B: Proofs 

Appendix C: Mathematical Induction 

Appendix D: Polynomials 


ELEMENTARY LINEAR ALGEBRA 

2nd Edition 

By Keith Nicholson, University of Calgary 

2004 / 608 pages / softcover 

ISBN: 9780070911420 

ISBN: 9780071234399 [IE] - GOP 

(McGraw-Hill Canada Title) 

www.mcgraw-hill.ca/college/nicholson 

CONTENTS 

Chapter 1 Linear Equations and Matrices: 

Matrices. 

Linear Equations. 

Homogeneous Systems. 

Matrix Multiplication. 

Matrix Inverses. 

Elementary Matrices. 

Lu-Factorization. 

Application ot Markov Chains. 

Chapter 2 Determinants and Eigenvalues: 

Cofactor Expansions. 

Determinants and Inversees. 

Diagonalization and Eigenvalues. 

Linear Dynamical Systems. 

Complex Eignevalues. 

Linear Recurrences. 

Polynomial Interpolation. 

Systems of Differential Equations. 

Chapter 3 Vector Geometry: 

Geometric Vectors. 

Dot Product and Projections. 

Lines and Planes. 

Matrix Transformation of R^2. 

The Cross Product: 

Optional. 

Chapter 4 The Vector Space R^n. 

Subspaces and Spanning. 

Linear Independence. 

Dimension. 

Rank. 

Orthogonality. 

Projections and Approximation. 

Orthogonal Diagonalization. 

Quadratic Forms. 

Linear Transformations. 

Complex Matrices. 

Singular Value Decomposition. 

Chapter 5 Vector Spaces: 

Examples and Basic Properties. 

Independence and Dimension. 

Linear Transformations. 

Isomorphisms and Matrices. 

Linear Operations and Similarity. 

Invariant Subspaces. 

General Inner Products. 

Appendix: 

A.1 Basic Trigonometry. 

112


A.2 Induction. 

A.3 Polynomials 

SCHAUM’S OUTLINE OF LINEAR ALGEBRA 

4th Edition 

By Seymour Lipschutz, Temple University-Philadelphia and Marc Lipson, 


2009 (July 2008) / 480 pages 

ISBN: 9780071543521 



course scope and sequence. The ideal review for hundreds of 

thousands of college and high school students who enroll in linear 

algebra courses. 

CONTENTS 

1. Vectors in R and C, Spatial Vectors 

2. Algebra of Matrices 

3. Systems of Linear Equations 

4. Vector Spaces 

5. Linear Mappings 

6. Linear Mappings and Matrices 

7. Inner Product Spaces, Orthogonality 

8. Determinants 

9. Diagonalization: Eigenvalues and Eigenvectors 

10. Canonical Forms 

11. Linear Functionals and the Dual Space 

12. Bilinear, Quadratic, and Hermitian Forms 

13. Linear Operators on Inner Product Spaces 

14. Multilinear Products 

SCHAUM’S EASY OUTLINES: LINEAR 

ALGEBRA 

By Seymour Lipschutz, Temple University - Philadelphia Marc Lipson, 


2003 / Softcover 

ISBN: 9780071398800 



For students looking for a quick nuts-and-bolts overview, it would have 

to be Schaum’s Easy Outline series. Every book in this series is a 

 

sor. With an emphasis on clarity and brevity, each new title features 

a streamlined and updated formatº and the absolute essence of the 

subject, presented in a concise and readily understandable form. 


highlights stress selected points from the text, illuminate keys to learning, 

and give students quick pointers to the essentials. 


LINEAR ALGEBRA 


1996 / 473 pages 

ISBN: 9780070380370 


CONTENTS 

Vectors and Matrix Algebra. 

Systems of Linear Equations. 

Square Matrices: Elementary Matrices. 

Vector Spaces and Subspaces. 

Basis and Dimension. 

Coordinates; Change of Basis. 

Inner Product Spaces; Orthogonality. 

Linear Mappings. 

Linear Mappings and Matrices. 

Determinants. 

Eigenvalues and Eigenvectors. 

Quadratic Forms and Symmetric Matrices. 


LINEAR ALGEBRA 

By Seymour Lipschultz, Temple University 

1989 / 496 pages 

ISBN: 9780070380233 


CONTENTS 

Vectors in R and C. 

Matrix Algebra. 

Systems of Linear Equations. 

Square Matrices. 

Determinants. 

Algebraic Structures. 

Vector Spaces and Subspaces. 

Linear Dependence, Basis, Dimension. 

Mappings. 

Linear Mappings. 

Spaces of Linear Mappings. 

Matrices and Linear Mappings. 

Change of Basis, Similarity. 

Inner Product Spaces, Orthogonality. 

Polynomials Over a Field. 

Eigenvalues and Eigenvectors. 

Diagonalization. 

Canonical Forms. 

Linear Functional and the Dual Space. 

Bilinear, Quadratic, and Hermitian Forms. 

Linear Operators on Inner Product Spaces. 

Applications to Geometry and Calculus. 

113



LINEAR ALGEBRA DEMYSTIFIED 

By David McMahon 

2006 / 255 pages 

ISBN: 9780071465793 


CONTENTS 

PREFACE 


Chapter 2: Matrix Algebra 

Chapter 3: Determinants 

Chapter 4: Vectors 

Chapter 5: Vector Spaces 

Chapter 6: Inner Product Spaces 

Chapter 7: Linear Transformations 

Chapter 8: The Eigenvalue Problem 

Chapter 9: Special Matrices 

Chapter 10: Matrix Decomposition 

FINAL EXAM 

HINTS AND SOLUTIONS 

REFERENCES 

INDEX 

Combinatorics 


INTRODUCTION TO ENUMERATIVE 

COMBINATORICS 

By Miklos Bona, University Of Florida @ Gainesville 

2007 (September 2005) / 544 pages / Hardcover 

ISBN: 9780073125619 

ISBN: 9780071254151 [IE] 

CONTENTS 

Foreword. 

Preface. 

Acknowledgments. 

I How: Methods. 

1 Basic Methods. 

1.1 When We Add and When We Subtract 

1.1.1 When We Add 

1.1.2 When We Subtract 

1.2 When We Multiply 

1.2.1 The Product Principle 

1.2.2 Using Several Counting Principles 

1.2.3 When Repetitions Are Not Allowed 

1.3 When We Divide 

1.3.1 The Division Principle 

1.3.2 Subsets 

1.4 Applications of Basic Counting Principles 

1.4.1 Bijective Proofs 

1.4.2 Properties of Binomial Coefficients 

1.4.3 Permutations With Repetition. 

1.5 The Pigeonhole Principle 

1.6 Notes 

1.7 Chapter Review 

1.8 Exercises 

1.9 Solutions to Exercises 

1.10 Supplementary Exercises. 

2 Direct Applications of Basic Methods 

2.1 Multisets and Compositions 

2.1.1 Weak Compositions 

2.1.2 Compositions 

2.2 Set Partitions 

2.2.1 Stirling Numbers of the Second Kind 

2.2.2 Recurrence Relations for Stirling Numbers of the Second Kind 

2.2.3 When the Number of Blocks Is Not Fixed 

2.3 Partitions of Integers 

2.3.1 Nonincreasing Finite Sequences of Integers 

2.3.2 Ferrers Shapes and Their Applications 

2.3.3 Excursion: Euler’s Pentagonal Number Theorem 

2.4 The Inclusion-Exclusion Principle 

2.4.1 Two Intersecting Sets 

2.4.2 Three Intersecting Sets 

2.4.3 Any Number of Intersecting Sets 

2.5 The Twelvefold Way 

2.6 Notes 


2.8 Exercises 


2.10 Supplementary Exercises 

3 Generating Functions 


3.1.1 Generalized Binomial Coefficients 

3.1.2 Formal Power Series 

3.2 Warming Up: Solving Recursions 

3.2.1 Ordinary Generating Functions 

3.2.2 Exponential Generating Functions 

3.3 Products of Generating Functions 



3.4 Excursion: Composition of Two Generating Functions 



3.5 Excursion: A Different Type of Generating Function 

3.6 Notes 


3.8 Exercises 



II What: Topics. 

4 Counting Permutations 

4.1 Eulerian Numbers 

4.2 The Cycle Structure of Permutations 

4.2.1 Stirling Numbers of the First Kind 

4.2.2 Permutations of a Given Type 

4.3 Cycle Structure and Exponential Generating Functions 

4.4 Inversions 

4.4.1 Counting Permutations with Respect to Inversions 

4.5 Notes 


4.7 Exercises 



5 Counting Graphs 

5.1 Counting Trees and Forests 

5.1.1 Counting Trees 

5.2 The Notion of Graph Isomorphisms 

5.3 Counting Trees on Labeled Vertices 

5.3.1 Counting Forests 

5.4 Graphs and Functions 

5.4.1 Acyclic Functions 

5.4.2 Parking Functions 

5.5 When the Vertices Are Not Freely Labeled 

5.5.1 Rooted Plane Trees 

114


5.5.2 Binary Plane Trees 

5.6 Excursion: Graphs on Colored Vertices 

5.6.1 Chromatic Polynomials 

5.6.2 Counting k-colored Graphs 

5.7 Graphs and Generating Functions 

5.7.1 Generating Functions of Trees 

5.7.2 Counting Connected Graphs 

5.7.3 Counting Eulerian Graphs 

5.8 Notes 


5.10 Exercises 



6 Extremal Combinatorics 

6.1 Extremal Graph Theory 

6.1.1 Bipartite Graphs 

6.1.2 Tur´an’s Theorem 

6.1.3 Graphs Excluding Cycles 

6.1.4 Graphs Excluding Complete Bipartite Graphs 

6.2 Hypergraphs 

6.2.1 Hypergraphs with Pairwise Intersecting Edges 

6.2.2 Hypergraphs with Pairwise Incomparable Edges 

6.3 Something Is More Than Nothing: Existence Proofs 

6.3.1 Property B 

6.3.2 Excluding Monochromatic Arithmetic Progressions 

6.3.3 Codes Over Finite Alphabets 

6.4 Notes 


6.6 Exercises 



III What Else: Special Topics. 

7 Symmetric Structures 

7.1 Hypergraphs with Symmetries 

7.2 Finite Projective Planes 

7.2.1 Excursion: Finite Projective Planes of Prime Power Order 

7.3 Error-Correcting Codes 

7.3.1 Words Far Apart 

7.3.2 Codes from Hypergraphs 

7.3.3 Perfect Codes 

7.4 Counting Symmetric Structures 

7.5 Notes 


7.7 Exercises 



8 Sequences in Combinatorics 

8.1 Unimodality 

8.2 Log-Concavity 

8.2.1 Log-Concavity Implies Unimodality 

8.2.2 The Product Property 

8.2.3 Injective Proofs 

8.3 The Real Zeros Property 

8.4 Notes 


8.6 Exercises 



9 Counting Magic Squares and Magic Cubes 

9.1 An Interesting Distribution Problem 

9.2 Magic Squares of Fixed Size 

9.2.1 The Case of n = 3 

9.2.2 The Function Hn(r) for Fixed n 

9.3 Magic Squares of Fixed Line Sum 

9.4 Why Magic Cubes Are Different 

9.5 Notes 


9.7 Exercises 


A The Method of Mathematical Induction. 

A.1 Weak Induction 

A.2 Strong Induction References 

Index 

List of Frequently Used Notation 

SCHAUM’S OUTLINE OF COMBINATORICS 

By V K Balakrishnan, University of Maine 

1995 / 320 pages 

ISBN: 9780070035751 


CONTENTS 

The Sum Rule and the Product Rule. 

Permutations and Combinations. 

The Pigeonhole Principle. 

Generalized Permutations and Combinations. 

Sequences and Selections. 

The Inclusion-Exclusion Principle. 

Generating Functions and Partitions of Integers. 

The Distribution Problem in Combinatorics. 

Recurrence Relations. 

Group Theory in Combinatorics--Including The Burnside-Froberius 

Theorem. 

Permutation Groups and Their Cycles Indices and Polya’s Enumeration 

Theorems. 

Advanced Engineering 

Mathematics 


MATHCAD: A TOOL FOR ENGINEERS AND 

SCIENTISTS (B.E.S.T. SERIES) 

2nd Edition 

by Philip J. Pritchard, Manhattan College 

2008 (August 2007) / Softcover / 224 pages 

ISBN: 9780077231569 (with CD-Rom) 

ISBN: 9780071266987 [IE] 

www.mhhe.com/best 

Mathcad: A Tool for Engineering Problem Solving explains how to 

use Mathcad 13 (Student and Standard), This book is current with 

the latest release of mathcad, with the focus on the fundamentals, is 

enriched with great motivating applications, solid homework problems, 

appealing to both engineers and scientists. 

CONTENTS 

1 What Is Mathcad and Why Use It? 

2 The Basics of Mathcad 

3 How to Graph Functions 

4 Symbolic and Numeric Calculus 

5 How to Solve Equations 

6 Vectors, Matrices, and More 

7 Solving Ordinary Differential Equations 

8 Doing Statistics with Mathcad 

9 Importing and Exporting, the Web, and Some Advanced Concepts 

115



SPREADSHEET TOOLS FOR ENGINEERS 

USING EXCEL 

3rd Edition 

by Byron S Gottfried, University of Pittsburgh-Pittsburgh 


ISBN: 9780072971842 

ISBN: 9780071106634 [IE] - Out of Print 

www.mhhe.com/gottfried3e 

CONTENTS 

Part I: Excel Fundamentals 

1. Engineering Analysis and Spreadsheets 

2. Creating an Excel Worksheet 

3. Editing an Excel Worksheet 

4. Graphing Data 

5. Organizing Data 

6. Transferring Data 

Part II: Engineering Applications 

7. Converting Units 

8. Analyzing Data Statistically 

9. Fitting Equations to Data 

10. Solving Single Equations 

11. Solving Simultaneous Equations 

12. Evaluating Integrals 

13. Making Logical Decisions (IF-THEN-ELSE) 

14. Recording and Running Macros 

15. Comparing Economic Alternatives 

16. Finding Optimum Solutions 

Appendix. 

Index 

HIGHER ENGINEERING MATHEMATICS 

By B.V. Ramana, JNTU College of Engineering-Kakinada 

2006 (July 2006) / 1312 pages 

ISBN: 9780070634190 

McGraw-Hill India Title 

www.mhhe.com/ramanahem 

CONTENTS 

Part A: Preliminaries 

Chapter 1. Vector Algebra, Theory of Equations, Complex Numbers 

Part B: Differential and Integral Calculus 

Chapter 2. Differential Calculus 

Chapter 3. Partial Differentiation 

Chapter 4. Maxima and Minima 

Chapter 5. Curve Tracing 

Chapter 6. Integral Calculus: Applications 

Chapter 7. Multiple Integrals 

Part C: Ordinary Differential Equations 

Chapter 8. Ordinary Differential Equations: First Order with Applications 

Chapter 9. Ordinary Differential Equations: Second and higher orders 

with Applications 

Chapter 10. Series Solutions 

Chapter 11. Special Functions 

Chapter 12. Laplace Transform 

Part D: Linear Algebra and Vector Calculus 

Chapter 13. Matrices 

Chapter 14. Eigen Values and Eigen Vectors 

Chapter 15. Vector Differential Calculus 

Chapter 16. Vector Integral Calculus 

Part E: Fourier Analysis and Partial Differential Equations 

Chapter 17. Fourier Series 

Chapter 18. Partial Differential Equations 

Chapter 19. Applications of PDE 

Chapter 20. Fourier Integral and Fourier Transform 

Chapter 21. Finite Differences And Z-transforms 

Part F: Complex Analysis 

Chapter 22. Complex Functions 

Chapter 23. Complex Integration 

Chapter 24. Theory of Residues 

Chapter 25. Conformal Mapping 

Part G: Probability and Statistics 

Chapter 26. Probability Theory 

Chapter 27. Probability Distributions 

Chapter 28. Sampling Distributions (SD) 

Chapter 29. Inferences concerning means and proportions 

Chapter 30. Line & Curve Fitting, Correlation and Regression 

Chapter 31. Joint Probability Distribution and Markov Chains 

Part H: Numerical Analysis 

Chapter 32. Numerical Analysis 

Chapter 33. Numerical Solutions of ODE and PDE 

Appendices 

A1: Basic Results 

A2: Statistical Tables 

A3: Bibliography 

A4: Index 

SCHAUM’S OUTLINE OF TENSOR 

CALCULUS 

By David Kay, Worcester Polytechnic 


ISBN: 9780071756037 


Schaum’s Outline of Tensor Calculus mirrors the course in scope 

and sequence to help enrolled students understand basic concepts 

and offer extra practice on all Tensor Calculus topics. This easy-tounderstand 

introduction for undergraduates and graduates proves 

fundamental for practitioners of theoretical physics and certain areas 

 

valuable for mathematicians. This study guide teaches all the basics 

and effective problem-solving skills too. 

CONTENTS 

1. The Einstein Summation Convention. 

2. Basic Linear Algebra for Tensors. 

3. General Tensors. 

4. Tensor Operations. 

5. Tests for Tensor Character. 

6. The Metric Tensor. 

7. The Derivative of a Tensor. 

8. Further Riemannian Geometry. 

9. Riemannian Curvature. 

10. Spaces of Zero Curvature. 

11. Tensors in Differential Geometry. 

12. Tensors in Mechanics. 

13. Tensors in Special Relativity. 

14. Tensors Without Coordinates. 

15. Introduction to Tensor Manifolds. 

116



MATHEMATICS FOR ENGINEERS AND 

SCIENTISTS 

By Murray R Spiegel, Rensselaer Polytechnic Institute 


ISBN: 9780071635400 


An update of this successful outline in Advanced Mathematics, 

 

concepts and methods are increasingly required as part of numerous 

courses in engineering and science. This outline provides a succinct 

review of applied math concepts in topics such as differential equations, 

Laplace transforms, vector analysis, fourier analysis, complex 

variables, and matrices. 

CONTENTS 

Review of Fundamental Concepts 

Ordinary Differential Equations 

Linear Differential Equations 

Laplace Transforms 

Vector Analysis 

Multiple, Line, and Surface Integrals and Integral Theorems 

Fourier Series 

Fourier Integrals 

Gamma, Beta, and Other Special Functions 

Bessel Functions 

Lengendre Functions and Other Orthogonal Functions of Partial Differential 

Equations 

Complex Variables and Conformal Mapping 

Complex Inversion Formula for Laplace Transforms 

Matrices 

Calculus of Variations 

SCHAUM’S OUTLINE OF TENSOR 

CALCULUS 

By David Kay, Worcester Polytechnic 

1988 / 224 pgaes 

ISBN: 9780070334847 


CONTENTS 

The Einstein Summation Convention. 

Basic Linear Algebra for Tensors. 

General Tensors. 

Tensor Operations. 

Tests for Tensor Character. 

The Metric Tensor. 

The Derivative of a Tensor. 

Further Riemannian Geometry. 

Riemannian Curvature. 

Spaces of Zero Curvature. 

Tensors in Differential Geometry. 

Tensors in Mechanics. 

Tensors in Special Relativity. 

Tensors Without Coordinates. 

Introduction to Tensor Manifolds. 

Graph Theory 


INTRODUCTION TO GRAPH THEORY 

By Gary Chartrand, Western Michigan University—Kalamazoo and Ping 

Zhang, Western Michigan University—Kalamazoo 

2005 (May 2004) / 464 pages 


ISBN: 9780071238229 [IE] 

CONTENTS 

1. Introduction: Graphs and Graph Models. Connected Graphs. 

Common Classes of Graphs. 

2. Degrees: The Degree of a Vertex. Regular Graphs. Degree 

Sequences. Excursion: Graphs and Matrices. Exploration: Irregular 

Graphs. 

3. Isomorphic Graphs: The Definition of Isomorphisms. Isomorphism 

as a Relation. Excursion: Recognition, Reconstruction, Solvability. 

Excursion: Graphs and Groups. 

4. Trees: Bridges. Trees. The Minimum Spanning Tree Problem. 

Excursion: The Number of Spanning Trees. Exploration: Comparing 

Trees. 

5. Connectivity: Cut-Vertices. Blocks. Connectivity. Menger’s Theorem. 

Exploration: Geodetic Sets. 

6. Traversability: Eulerian Graphs. Hamiltonian Graphs. Exploration: 

Hamiltonian Walks and Numbers. Excursion: The Early Books 

of Graph Theory. 

7. Digraphs: Strong Digraphs. Tournaments. Excursion: How to Make 

Decisions. Exploration: Wine Bottle Problems. 

8. Matchings and Factorization: Matchings. Factorizations. Decompositions 

and Graceful Labelings. Excursion: Instant Insanity. 

Excursion: The Petersen Graph. Exploration: -Labeling of Graphs. 

9. Planarity: Planar Graphs. Embedding Graphs on Surfaces. Excursion: 

Graphs Minors. Exploration: Embedding Graphs in Graphs. 

10. Coloring Graphs: The Four Color Problem. Vertex Coloring. 

Edge Coloring. Excursion: The Heawood Map-Coloring Theorem. 

Exploration: Local Coloring. 

11. Ramsey Numbers: The Ramsey Number of Graphs. Turan’s 

Theorem. Exploration: Rainbow Ramsey Numbers. Excursion: 

Erd?umbers. 

12. Distance: The Center of a Graph. Distant Vertices. Excursion: 

Locating Numbers. Excursion: Detour Distance and Directed Distance. 

Exploration: The Channel Assignment Problem. Exploration: Distance 

Between Graphs. 

13. Domination: The Domination Number of a Graph. Exploration: 

Stratification. Exploration: Lights Out. Excursion: And Still It Grows 

More Colorful. 

Appendix 1. Sets and Logic. 

Appendix 2. Equivalence Relations and Functions. 

Appendix 3. Methods of Proof. 

Answers and Hints to Odd-Numbered Exercises. 

References. 

Index of Symbols. 

Index of Mathematical Terms 

117



APPLIED AND ALGORITHMIC GRAPH 

THEORY 

By Gary Chartrand, Western Michigan University, and Ortrud Oellermann, 

University of Natal, South Africa 

1993 / 432 pages 


ISBN: 9780071125758 [IE] 

CONTENTS 

1 An Introduction to Graphs 

2 An Introduction to Algorithms 

3 Trees 

4 Paths and Distance and Graphs 

5 Networks 

6 Matchings and Factorizations 

7 Eulerian Graphs 

8 Hamiltonian Graphs 

9 Planar Graphs 

10 Coloring Graphs 

11 Digigraphs 

12 Extremal Graph Theory 

SCHAUM’S OUTLINE OF GRAPH THEORY 

Including Hundreds of Solved Problems 

By V K Balakrishnan, University of Maine 

1997 / 288 pages 

ISBN: 9780070054899 


CONTENTS 

Graphs and Digraphs. 

Connectivity. 

Eulerian and Hamiltonian Graphs. 

Optimization Involving Trees. 

Shortest Path Problems. 

Flow and Connectivity. 

Planarity and Duality. 

Graph Colorings. 

Additional Topics. 

List of Technical Terms and Symbols Used. 

Introductory Analysis 


PRINCIPLES OF MATHEMATICAL ANALYSIS 

3rd Edition 

By Walter Rudin, University of Wisconsin-Madison 

1976 / 325 pages 

ISBN: 9780070542358 

ISBN: 9780070856134 [IE] 

CONTENTS 

Chapter 1: The Real Numbers: 

Section 1.1 Sets. 

Section 1.2 Functions. 

Section 1.3 Algebraic and order properties. 

Section 1.4 The positive integers. 

Section 1.5 The least upper bound axiom. 

Chapter 2: Sequences: 

Section 2.1 Sequences and limits. 

Section 2.2 Limit theorems. 

Section 2.3 Monotonic sequences. 

Section 2.4 Sequences defined inductively. 

Section 2.5 Sequences, Cauchy sequences. 

Section 2.6 Infinite limits. 

Chapter 3: Functions and Continuity: 

Section 3.1 Limit of a function. 

Section 3.2 Limit theorems. 

Section 3.3 Other limits. 

Section 3.4 Continuity. 

Section 3.5 Intermediate values, extreme values. 

Section 3.6 Uniform continuity. 

Chapter 4: The Derivative: 

Section 4.1 Definition of the derivative. 

Section 4.2 Rules for differentiation. 

Section 4.3 The Mean Value Theorem. 

Section 4.4 Inverse functions. 

Chapter 5: The Integral: 

Section 5.1 The definition of the integral. 

Section 5.2 Properties of the integral. 

Section 5.3 Existence theory. 

Section 5.4 The Fundamental Theorem of Calculus. 

Section 5.5 Improper integrals. 

Chapter 6: Infinite Series: 

Section 6.1 Basic theory. 

Section 6.2 Absolute convergence. 

Section 6.3 Power series. 

Section 6.4 Taylor series. 

Chapter 7: Sequences and Series of Functions: 

Section 7.1 Uniform convergence. 

Section 7.2 Consequences of uniform convergence. 

Section 7.3 Two examples. 

Solutions and Hints for Selected Problems. 

Index 

REVIEW COPY 










118


Advanced Calculus 

History Of Mathematics 


CALCULUS 

3rd Edition 

By Robert Wrede and Murray Spiegel 

2010 (January 2010) / 456 pages 

ISBN: 9780071623667 


Schaum’s Outline of Advanced Calculus mirrors the course in scope 

and sequence to help you understand basic concepts and offer extra 

practice on topics such as derivatives, integrals, multiple integrals, 

applications of partial derivatives, vectors, improper integrals, and 

Fourier series. Coverage will also include linear independence and 

linear dependence of a set of vectors, method of Lagrange multipliers 

for maxima and minima, the divergence theorem, and orthogonality 

conditions for the sine and cosine functions. 

CONTENTS 

1. Numbers 

2. Sequences 

3. Functions, Limits, and Continuity 

4. Derivatives 

5. Integrals 


7. Vectors 

8. Applications of Partial Derivatives 

9. Multiple Integrals 

10. Line Integrals, Surface Integrals, and Integral Theorems 



13. Fourier Series 

14. Fourier Integrals 

15. Gamma and Beta Functions 

16. Functions of a Complex Variable 

SCHAUM’S OUTLINE OF CALCULUS OF 

FINITE DIFFERENCES AND DIFFERENCE 

EQUATIONS 


1971 / 272 pages 

ISBN: 9780070602182 


CONTENTS 

The Difference Calculus. 

Applications of the Difference Calculus. 

The Sum Calculus. 

Applications of the Sum Calculus. 

Difference Equations. 

Applications of Difference Equations. 


NEW *9780073383156* 

THE HISTORY OF 

MATHEMATICS 

An Introduction, 7th Edition 

By David M. Burton, University Of New Hampshire 


ISBN: 9780073383156 

ISBN: 9780071289207 [IE] 

The History of Mathematics: An Introduction, Seventh Edition, is written 

for the one- or two-semester math history course taken by juniors 

or seniors, and covers the history behind the topics typically covered 

in an undergraduate math curriculum or in elementary schools or high 

schools. Elegantly written in David Burton’s imitable prose, this classic 

text provides rich historical context to the mathematics that undergrad 

math and math education majors encounter every day. Burton illuminates 

the people, stories, and social context behind mathematics’ 

greatest historical advances while maintaining appropriate focus on 

the mathematical concepts themselves. Its wealth of information, 

mathematical and historical accuracy, and renowned presentation 

make The History of Mathematics: An Introduction, Seventh Edition 

a valuable resource that teachers and students will want as part of 

a permanent library. 

CONTENTS 

Preface 

1 Early Number Systems and Symbols 

2 Mathematics in Early Civilizations 

3 The Beginnings of Greek Mathematics 

4 The Alexandrian School: Euclid 

5 The Twilight of Greek Mathematics: Diophantus 

6 The First Awakening: Fibonacci 

7 The Renaissance of Mathematics: Cardan and Tartaglia 

8 The Mechanical World: Descartes and Newton 

9 The Development of Probability Theory: Pascal, Bernoulli, and 

Laplace 

10 The Revival of Number Theory: Fermat, Euler, and Gauss 

11 Nineteenth-Century Contributions: Lobachevsky to Hilbert 

12 Transition to the Twenthieth Century: Cantor and Kronecker 

13 Extensions and Generalizations: Hardy, Hausdorff, and Noether 

A Few Recent Advances 

General Bibliography 

Additional Reading 

The Greek Alphabet 

Solutions to Selected Problems 

Index 

119


Numerical Analysis 

Boundary Value Problems. 

Monte Carlo Methods. 


ELEMENTARY NUMERICAL ANALYSIS 

An Algorithmic Approach, 3rd Edition 

By Samuel D. Conte, Purdue University, Carl de Boor, University of 

Wisconsin-Madison 

1980 / 408 pages 


ISBN: 9780070662285 [IE] 

CONTENTS 

1 Number Systems and Errors 

2 Interpolation by Polynomial 

3 The Solution of Nonlinear Equations 

4 Matrices and Systems of Linear Equations 

5 Systems of Equations and Unconstrained Optimization 

6 Approximation 

7 Differentiation and Integration 

8 The Solution of Differential Equations 


Appendix: Subroutine Libraries 

References 

Index 

SCHAUM’S OUTLINE OF NUMERICAL 

ANALYSIS 

2nd Edition 

By Francis Scheid, Boston University 

1988 / 471 pages 

ISBN: 9780070552210 


CONTENTS 

What Is Numerical Analysis? 

The Collocation Polynomial. 

Finite Differences. 

Factorial Polynomials. 

Summation. 

The Newton Formula. 

Operators and Collocation Polynomials. 

Unequally-Spaced Arguments. 

Splines. 

Osculating Polynomials. 

The Taylor Polynomial. 

Interpolation. 

Numerical Differentiation. 

Numerical Integration. 

Gaussian Integration. 

Singular Integrals. 

Sums and Series. 

Difference Equations. 


Differential Problems of Higher Order. 

Least-Squares Polynomial Approximation. 

Min-Max Polynomial Approximation. 

Approximation By Rational Functions. 

Trigonometric Approximation. 

Nonlinear Algebra. 

Linear Systems. 

Linear Programming. 

Overdetermined Systems. 

Number Theory 


NEW *9780073383149* 

ELEMENTARY NUMBER 

THEORY 

7th Edition 

By David M. Burton, University Of New Hampshire 

2011 (January 2010) / 448 pages 

ISBN: 9780073383149 

ISBN: 9780071289191 [IE] 

Elementary Number Theory, Seventh Edition, is written for the onesemester 

undergraduate number theory course taken by math majors, 

secondary education majors, and computer science students. This 

contemporary text provides a simple account of classical number 

theory, set against a historical background that shows the subject’s 

evolution from antiquity to recent research. Written in David Burton’s 

engaging style, Elementary Number Theory reveals the attraction that 

has drawn leading mathematicians and amateurs alike to number 

theory over the course of history. 


Expanded Cryptography Coverage - Coverage on public key 

cryptosystems has been considerably expanded in the Seventh 

Edition into a new chapter, ¿Introduction to Cryptography,” reflecting 

the profound recent influence of fast computers on on number theory 

and its applications. 

New Coverage of Farey fractions. The Seventh Edition expands 

the coverage of Farey fractions which provides a a straightforward 

means of closely approximating irrational numbers by rational values. 

CONTENTS 

Preface 

New to this Edition 

1 Preliminaries 

1.1 Mathematical Induction 


2 Divisibility Theory in the Integers 

2.1 Early Number Theory 

2.2 The Division Algorithm 

2.3 The Greatest Common Divisor 

2.4 The Euclidean Algorithm 

2.5 The Diophantine Equation 

3 Primes and Their Distribution 

3.1 The Fundamental Theorem of Arithmetic 

3.2 The Sieve of Eratosthenes 

3.3 The Goldbach Conjecture 

4 The Theory of Congruences 

4.1 Carl Friedrich Gauss 

4.2 Basic Properties of Congruence 

120


4.3 Binary and Decimal Representations of Integers 

4.4 Linear Congruences and the Chinese Remainder Theorem 

5 Fermat’s Theorem 

5.1 Pierre de Fermat 

5.2 Fermat’s Little Theorem and Pseudoprimes 

5.3 Wilson’s Theorem 

5.4 The Fermat-Kraitchik Factorization Method 

6 Number-Theoretic Functions 

6.1 The Sum and Number of Divisors 

6.2 The Möbius Inversion Formula 

6.3 The Greatest Integer Function 

6.4 An Application to the Calendar 

7 Euler’s Generalization of Fermat’s Theorem 

7.1 Leonhard Euler 

7.2 Euler’s Phi-Function 

7.3 Euler’s Theorem 

7.4 Some Properties of the Phi-Function 

8 Primitive Roots and Indices 

8.1 The Order of an Integer Modulo n 

8.2 Primitive Roots for Primes 

8.3 Composite Numbers Having Primitive Roots 

8.4 The Theory of Indices 

9 The Quadratic Reciprocity Law 

9.1 Euler’s Criterion 

9.2 The Legendre Symbol and Its Properties 

9.3 Quadratic Reciprocity 

9.4 Quadratic Congruences with Composite Moduli 

10 Introduction to Cryptography 

10.1 From Caesar Cipher to Public Key Cryptography 

10.2 The Knapsack Cryptosystem 

10.3 An Application of Primitive Roots to Cryptography 

11 Numbers of Special Form 

11.1 Marin Mersenne 

11.2 Perfect Numbers 

11.3 Mersenne Primes and Amicable Numbers 

11.4 Fermat Numbers 

12 Certain Nonlinear Diophantine Equations 

12.1 The Equation 

12.2 Fermat’s Last Theorem 

13 Representation of Integers as Sums of Squares 

13.1 Joseph Louis Lagrange 

13.2 Sums of Two Squares 

13.3 Sums of More Than Two Squares 

14 Fibonacci Numbers 

14.1 Fibonacci 

14.2 The Fibonacci Sequence 

14.3 Certain Identities Involving Fibonacci Numbers 

15 Continued Fractions 

15.1 Srinivasa Ramanujan 

15.2 Finite Continued Fractions 

15.3 Infinite Continued Fractions 

15.4 Farey Fractions 

15.5 Pell’s Equation 

16 Some Recent Developments 

16.1 Hardy, Dickson, and Erdös 

16.2 Primality Testing and Factorization 

16.3 An Application to Factoring: Remote Coin Flipping 

16.4 The Prime Number Theorem and Zeta Function 

Miscellaneous Problems 

Appendixes 

General References 

Suggested Further Reading 

Tables 

Answers to Selected Problems 

Index 

Advanced Geometry 


GEOMETRY 

By Martin M. Lipschutz, Hahnemann Medical College 

1969 / 288 pages 

ISBN: 9780070379855 


CONTENTS 

Vectors. 

Vector Functions of Real Variable. 

Concept of Curve. 

Curvature and Torsion. 

Theory of Curves. 

Elementary Topology in Euclidean Spaces. 

Vector Functions of Vector Variable. 

Concept of Curve. 

First and Second Fundamental Forms. 

Theory of Surfaces. 

Tensor Analysis. 

Intrinsic Geometry. 

Appendix. 

Existence Theorem for Curves. 

Existence Theorem for Surfaces. 

Complex Analysis 


COMPLEX VARIABLES AND APPLICATIONS 

8th Edition 

By James Ward Brown, University of Michigan-Dearborn and Ruel V 

Churchill (deceased) 

2009 (January 2008) / 504 pages 

ISBN: 9780073051949 

ISBN: 9780071263283 [IE] 

Complex Variables and Applications, 8e will serve, just as the earlier 

editions did, as a textbook for an introductory course in the theory 

and application of functions of a complex variable. This new edition 

preserves the basic content and style of the earlier editions. The text 

is designed to develop the theory that is prominent in applications of 

 

of residues and conformal mappings. To accommodate the different 

calculus backgrounds of students, footnotes are given with references 

to other texts that contain proofs and discussions of the more delicate 

results in advanced calculus. Improvements in the text include 

extended explanations of theorems, greater detail in arguments, and 

the separation of topics into their own sections. 

CONTENTS 

1 Complex Numbers 

Sums and Products 

Basic Algebraic Properties 

Further Properties 

Moduli 

Complex Conjugates 

Exponential Form 

Products and Quotients in Exponential Form 

121


Roots of Complex Numbers 

Examples 

Regions in the Complex Plane 

2 Analytic Functions 

Functions of a Complex Variable 

Mappings 

Mappings by the Exponential Function 

Limits 

Theorems on Limits 

Limits Involving the Point at Infinity 

Continuity 

Derivatives 

Differentiation Formulas 

Cauchy–Riemann Equations 

Sufficient Conditions for Differentiability 

Polar Coordinates 

Analytic Functions 

Examples 

Harmonic Functions 

Uniquely Determined Analytic Functions 

Reflection Principle 

3 Elementary Functions 

The Exponential Function 

The Logarithmic Function 

Branches and Derivatives of Logarithms 

Some Identities Involving Logarithms 

Complex Exponents 

Trigonometric Functions 

Hyperbolic Functions 

Inverse Trigonometric and Hyperbolic Functions 

4 Integrals 

Derivatives of Functions w(t) 

Definite Integrals of Functions w(t) 

Contours 

Contour Integrals 

Examples 

Upper Bounds for Moduli of Contour Integrals 

Antiderivatives 

Examples 

Cauchy–Goursat Theorem 

Proof of the Theorem 

Simply and Multiply Connected Domains 

Cauchy Integral Formula 

Derivatives of Analytic Functions 

Liouville’s Theorem and the Fundamental Theorem of Algebra 

Maximum Modulus Principle 

5 Series 

Convergence of Sequences 

Convergence of Series 

Taylor Series 

Examples 

Laurent Series 

Examples 

Absolute and Uniform Convergence of Power Series 

Continuity of Sums of Power Series 

Integration and Differentiation of Power Series 

Uniqueness of Series Representations 

Multiplication and Division of Power Series 

6 Residues and Poles 

Residues 

Cauchy’s Residue Theorem 

Using a Single Residue 

The Three Types of Isolated Singular Points 

Residues at Poles 

Examples 

Zeros of Analytic Functions 

Zeros and Poles 

Behavior of f Near Isolated Singular Points 

7 Applications of Residues 

Evaluation of Improper Integrals 

Example 

Improper Integrals from Fourier Analysis 

Jordan’s Lemma 

Indented Paths 

An Indentation Around a Branch Point 

Integration Along a Branch Cut 

Definite Integrals Involving Sines and Cosines 

Argument Principle 

Rouché’s Theorem 

Inverse Laplace Transforms 

Examples 

8 Mapping by Elementary Functions 

Linear Transformations 

The Transformation w = 1/z 

Mappings by 1/z 

Linear Fractional Transformations 

An Implicit Form 

Mappings of the Upper Half Plane 

The Transformation w = sin z 

Mappings by z2 and Branches of z1/2 

Square Roots of Polynomials 

Riemann Surfaces 

Surfaces for Related Functions 

9 Conformal Mapping 

Preservation of Angles 

Scale Factors 

Local Inverses 

Harmonic Conjugates 

Transformations of Harmonic Functions 

Transformations of Boundary Conditions 

10 Applications of Conformal Mapping 

Steady Temperatures 

Steady Temperatures in a Half Plane 

A Related Problem 

Temperatures in a Quadrant 

Electrostatic Potential 

Potential in a Cylindrical Space 

Two-Dimensional Fluid Flow 

The Stream Function 

Flows Around a Corner and Around a Cylinder 

11 The Schwarz–Christoffel Transformation 

Mapping the Real Axis onto a Polygon 

Schwarz–Christoffel Transformation 

Triangles and Rectangles 

Degenerate Polygons 

Fluid Flow in a Channel Through a Slit 

Flow in a Channel with an Offset 

Electrostatic Potential about an Edge of a Conducting Plate 

12 Integral Formulas of the Poisson Type 

Poisson Integral Formula 

Dirichlet Problem for a Disk 

Related Boundary Value Problems 

Schwarz Integral Formula 

Dirichlet Problem for a Half Plane 

Neumann Problems 

Appendixes 

Bibliography 

Table of Transformations of Regions 

Index 

122




3rd Edition 

By Walter Rudin, University of Wisconsin 

1987 / 483 pages 

ISBN: 9780070542341 

ISBN: 9780071002769 [IE] 

CONTENTS 

Preface. 

Prologue: The Exponential Function. 

Chapter 1: Abstract Integration: 

Set-theoretic notations and terminology. The concept of measurability. 

Simple functions. Elementary properties of measures. Arithmetic in 

[0, infinity]. Integration of positive functions. Integration of complex 

functions. The role played by sets of measure zero. Exercises. 

Chapter 2: Positive Borel Measures: 

Vector spaces. Topological preliminaries. The Riesz representation 

theorem. Regularity properties of Borel measures. Lebesgue measure. 

Continuity properties of measurable functions. Exercises. 

Chapter 3: L^p-Spaces: 

Convex functions and inequalities. The L^p-spaces. Approximation 

by continuous functions. Exercises. 

Chapter 4: Elementary Hilbert Space Theory: 

Inner products and linear functionals. Orthonormal sets. Trigonometric 

series. Exercises. 

Chapter 5: Examples of Banach Space Techniques: 

Banach spaces. Consequences of Baire’s theorem. Fourier series 

of continuous functions. Fourier coefficients of L-functions. The 

Hahn-Banach theorem. An abstract approach to the Poisson integral. 

Exercises. 

Chapter 6: Complex Measures: 

Total variation. Absolute continuity. Consequences of the Radon- 

Nikodym theorem. Bounded linear functionals on L^p. The Riesz 

representation theorem. Exercises. 


Derivatives of measures. The fundamental theorem of Calculus. Differentiable 

transformations. Exercises. 

Chapter 8: Integration on Product Spaces: 

Measurability on cartesian products. Product measures. The Fubini 

theorem. Completion of product measures. Convolutions. Distribution 

functions. Exercises. 

Chapter 9: Fourier Transforms: 

Formal properties. The inversion theorem. The Plancherel theorem. 

The Banach algebra L. Exercises. 

Chapter 10: Elementary Properties of Holomorphic Functions: 

Complex differentiation. Integration over paths. The local Cauchy 

theorem. The power series representation. The open mapping theorem. 

The global Cauchy theorem. The calculus of residues. Exercises. 

Chapter 11: Harmonic Functions: 

The Cauchy-Riemann equations. The Poisson integral. The mean 

value property. Boundary behavior of Poisson integrals. Representation 

theorems. Exercises. 

Chapter 12: The Maximum Modulus Principle: 

Introduction. The Schwarz lemma. The Phragmen-Lindel’s Method. 

An interpolation theorem. A converse of the maximum modulus 

theorem. Exercises. 

Chapter 13: Approximation by Rational Functions: 

Preparation. Runge’s theorem. The Mittag-Leffler theorem. Simply 

connected regions. Exercises. 

Chapter 14: Conformal Mapping: 

Preservation of angles. Linear fractional transformations. Normal 

families. The Riemann mapping theorem. The class. Continuity at the 

boundary. Conformal mapping of an annulus. Exercises. 

Chapter 15: Zeros of Holomorphic Functions: 

Infinite Products. The Weierstrass factorization theorem. An interpolation 

problem. Jensen’s formula. Blaschke products. The M’zas 


Chapter 16: Analytic Continuation: 

Regular points and singular points. Continuation along curves. The 

monodromy theorem. Construction of a modular function. The Picard 


Chapter 17: H^p-Spaces: 

Subharmonic functions . The spaces H^p and N. The theorem of F. 

and M. Riesz. Factorization theorems. The shift operator. Conjugate 


Chapter 18: Elementary Theory of Banach Algebras: 

Introduction. The invertible elements. Ideals and homomorphisms. 

Applications. Exercises. 

Chapter 19: Holomorphic Fourier Transforms: 

Introduction. Two theorems of Paley and Wiener. Quasi-analytic 

classes. The Denjoy-Carleman theorem. Exercises. 

Chapter 20: Uniform Approximation by Polynomials: 

Introduction. Some lemmas. Mergelyan’s theorem. Exercises. 

Appendix: 

Hausdorff’s Maximality Theorem. Notes and Comments. Bibliography. 

List of Special Symbols. Index 


COMPLEX ANALYSIS 

3rd Edition 

By Lars Ahlfors, Harvard University 

1979 / 336 pages 

ISBN: 9780070006577 

ISBN: 9780070850088 [IE] 

CONTENTS 

Chapter 1: Complex Numbers: 

1 The Algebra of Complex Numbers. 

2 The Geometric Representation of Complex Numbers. 

Chapter 2: Complex Functions: 

1 Introduction to the Concept of Analytic Function. 

2 Elementary Theory of Power Series. 

3 The Exponential and Trigonometric Functions. 

Chapter 3: Analytic Functions as Mappings: 

1 Elementary Point Set Topology. 

2 Conformality. 

3 Linear Transformations. 

4 Elementary Conformal Mappings. 

Chapter 4: Complex Integration: 

1 Fundamental Theorems. 

2 Cauchy’s Theorem for a Rectangle. 

3 Local Properties of Analytical Functions. 

4 The General Form of Cauchy’s Theorem. 

5 The Calculus of Residues. 

6 Harmonic Functions. 

Chapter 5: Series and Product Developments: 

1 Power Series Expansions. 

2 Partial Fractions and Factorization. 

3 Entire Functions. 

4 The Riemann Zeta Function. 

5 Normal Families. 

Chapter 6: Conformal Mapping, Dirichlet’s Problem: 

1 The Riemann Mapping Theorem. 

2 Conformal Mapping of Polygons. 

3 A Closer Look at Harmonic Functions. 

4 The Dirichlet Problem. 

5 Canonical Mappings of Multiply Connected Regions. 

Chapter 7: Elliptic Functions: 

1 Simply Periodic Functions. 

2 Doubly Periodic Functions. 

3 The Weierstrass Theory. 

Chapter 8: Global Analytic Functions: 

1 Analytic Continuation. 

2 Algebraic Functions. 

3 Picard’s Theorem. 

4 Linear Differential Equations. 

Index 

123


COMPLEX VARIABLES DEMYSTIFIED 

by David McMahon 


ISBN: 9780071549202 


Ready to learn the fundamentals of complex variables but can’t seem 

to get your brain to function on the right level? No problem! Add Com- 

 

increase your chances of understanding this fascinating subject. Written 

in an easy-to-follow format, this book begins by covering complex 

numbers, functions, limits, and continuity, and the Cauchy-Riemann 

equations. You’ll delve into sequences, Laurent series, complex 

integration, and residue theory. Then it’s on to conformal mapping, 

transformations, and boundary value problems. Hundreds of examples 

and worked equations make it easy to understand the material, 

 

Simple enough for a beginner, but challenging enough for an ad- 

 

for understanding this essential mathematics topic. 

CONTENTS 

Preface 

Chapter 1: Complex Numbers 

Chapter 2: Functions, Limits, and Continuity 

Chapter 3: The Derivative and Analytic Functions 

Chapter 4: Elementary Functions 

Chapter 5: Sequences and Series 

Chapter 6: Complex Integration 

Chapter 7: Residue Theory 

Chapter 8: More Complex Integration and the Laplace Transformation 

Chapter 9: Mapping and Transformations 

Chapter 10: The Schwarz-Christoffel Transformation 

Chapter 11. The Gamma and Zeta Functions 

Chapter 12. Boundary Value Problems 

Final Exam 

Quiz Solutions 

Final Exam Solutions 

Bibliography 

Index 

SCHAUM’S OUTLINE OF COMPLEX 

VARIABLES 

2nd Edition 

By Murray R Spiegel, formerly of Rensselaer Polytechnic Institute 

2009 (May 2009) / 320 pages 

ISBN: 9780071615693 


 

conform to the current curriculum. Complex variables are essential to 

the work of engineers, physicists, mathematicians, and other scien- 

 

 

 

Functional Analysis 


FUNCTIONAL ANALYSIS 

2nd Edition 

by Walter Rudin, University of Wisc 

1991/ Hardcover / 448 pages 


ISBN: 9780071009447 [IE] 

CONTENTS 

Preface. 

PART ONE: GENERAL THEORY 

1. Topological Vector Space 

Introduction 

Separation properties 

Linear Mappings 

Finite-dimensional spaces 

Metrization 

Boundedness and continuity 

Seminorms and local convexity 

Quotient spaces 

Examples 

Exercises 

2. Completeness 

Baire category 

The Banach-Steinhaus theorem 

The open mapping theorem 

The closed graph theorem 

Bilinear mappings 

Exercises 

3. Convexity 

The Hahn-Banach theorems 

Weak topologies 

Compact convex sets 

Vector-valued integration 

Holomorphic functions 

Exercises 

4. Duality in Banach Spaces 

The normed dual of a normed space 

Adjoints 

Compact operators 

Exercises 

5. Some Applications 

A continuity theorem 

Closed subspaces of Lp-spaces 

The range of a vector-valued measure 

A generalized Stone-Weierstrass theorem 

Two interpolation theorems 

Kakutani’s fixed point theorem 

Haar measure on compact groups 

Uncomplemented subspaces 

Sums of Poisson kernels 

Two more fixed point theorems 

Exercises 

PART TWO: DISTRIBUTIONS AND FOURIER TRANSFORMS 

6. Test Functions and Distributions 

Introduction 

Test function spaces 

Calculus with distributions 

Localization 

Supports of distributions 

Distributions as derivatives 

Convolutions 

Exercises 

124


7. Fourier Transforms 

Basic properties 

Tempered distributions 

Paley-Wiener theorems 

Sobolev’s lemma 

Exercises 

8. Applications to Differential Equations 

Fundamental solutions 

Elliptic equations 

Exercises 

9. Tauberian Theory 

Wiener’s theorem 

The prime number theorem 

The renewal equation 

Exercises 

PART THREE: BANACH ALGEBRAS AND SPECTRAL THEORY 

10. Banach Algebras 

Introduction 

Complex homomorphisms 

Basic properties of spectra 

Symbolic calculus 

The group of invertible elements 

Lomonosov’s invariant subspace theorem 

Exercises 

11. Commutative Banach Algebras 

Ideals and homomorphisms 

Gelfand transforms 

Involutions 

Applications to noncommutative algebras 

Positive functionals 

Exercises 

12. Bounded Operators on a Hillbert Space 

Basic facts 

Bounded operators 

A commutativity theorem 

Resolutions of the identity 

The spectral theorem 

Eigenvalues of normal operators 

Positive operators and square roots 

The group of invertible operators 

A characterization of B*-algebras 

An ergodic theorem 

Exercises 

13. Unbounded Operators 

Introduction 

Graphs and symmetric operators 

The Cayley transform 

Resolutions of the identity 

The spectral theorem 

Semigroups of operators 

Exercises 

Appendix A: Compactness and Continuity 

Appendix B: Notes and Comments 

Bibliography 


Index 

Real Analysis 



3rd Edition 

By Walter Rudin, University of Wisconsin 

1987 / 483 pages 

ISBN: 9780070542341 

ISBN: 9780071002769 [IE] 

CONTENTS 

Preface. 

Prologue: The Exponential Function. 

Chapter 1: Abstract Integration: 

Set-theoretic notations and terminology. The concept of measurability. 

Simple functions. Elementary properties of measures. Arithmetic in 

[0, infinity]. Integration of positive functions. Integration of complex 

functions. The role played by sets of measure zero. Exercises. 

Chapter 2: Positive Borel Measures: 

Vector spaces. Topological preliminaries. The Riesz representation 

theorem. Regularity properties of Borel measures. Lebesgue measure. 

Continuity properties of measurable functions. Exercises. 

Chapter 3: L^p-Spaces: 

Convex functions and inequalities. The L^p-spaces. Approximation 

by continuous functions. Exercises. 

Chapter 4: Elementary Hilbert Space Theory: 

Inner products and linear functionals. Orthonormal sets. Trigonometric 

series. Exercises. 

Chapter 5: Examples of Banach Space Techniques: 

Banach spaces. Consequences of Baire’s theorem. Fourier series 

of continuous functions. Fourier coefficients of L-functions. The 

Hahn-Banach theorem. An abstract approach to the Poisson integral. 

Exercises. 

Chapter 6: Complex Measures: 

Total variation. Absolute continuity. Consequences of the Radon- 

Nikodym theorem. Bounded linear functionals on L^p. The Riesz 

representation theorem. Exercises. 


Derivatives of measures. The fundamental theorem of Calculus. Differentiable 

transformations. Exercises. 

Chapter 8: Integration on Product Spaces: 

Measurability on cartesian products. Product measures. The Fubini 

theorem. Completion of product measures. Convolutions. Distribution 


Chapter 9: Fourier Transforms: 

Formal properties. The inversion theorem. The Plancherel theorem. 

The Banach algebra L. Exercises. 

Chapter 10: Elementary Properties of Holomorphic Functions: 

Complex differentiation. Integration over paths. The local Cauchy 

theorem. The power series representation. The open mapping theorem. 

The global Cauchy theorem. The calculus of residues. Exercises. 

Chapter 11: Harmonic Functions: 

The Cauchy-Riemann equations. The Poisson integral. The mean 

value property. Boundary behavior of Poisson integrals. Representation 

theorems. Exercises. 

Chapter 12: The Maximum Modulus Principle: 

Introduction. The Schwarz lemma. The Phragmen-Lindel’s Method. 

An interpolation theorem. A converse of the maximum modulus 


Chapter 13: Approximation by Rational Functions: 

Preparation. Runge’s theorem. The Mittag-Leffler theorem. Simply 

connected regions. Exercises. 

Chapter 14: Conformal Mapping: 

Preservation of angles. Linear fractional transformations. Normal 

families. The Riemann mapping theorem. The class. Continuity at the 

125


boundary. Conformal mapping of an annulus. Exercises. 

Chapter 15: Zeros of Holomorphic Functions: 

Infinite Products. The Weierstrass factorization theorem. An interpolation 

problem. Jensen’s formula. Blaschke products. The M’zas 


Chapter 16: Analytic Continuation: 

Regular points and singular points. Continuation along curves. The 

monodromy theorem. Construction of a modular function. The Picard 


Chapter 17: H^p-Spaces: 

Subharmonic functions . The spaces H^p and N. The theorem of F. 

and M. Riesz. Factorization theorems. The shift operator. Conjugate 


Chapter 18: Elementary Theory of Banach Algebras: 

Introduction. The invertible elements. Ideals and homomorphisms. 

Applications. Exercises. 

Chapter 19: Holomorphic Fourier Transforms: 

Introduction. Two theorems of Paley and Wiener. Quasi-analytic 

classes. The Denjoy-Carleman theorem. Exercises. 

Chapter 20: Uniform Approximation by Polynomials: 

Introduction. Some lemmas. Mergelyan’s theorem. Exercises. 

Appendix: 

Hausdorff’s Maximality Theorem. Notes and Comments. Bibliography. 

List of Special Symbols. Index 

Mathematical - References 

6. Financial Tables 


SCHAUM’S EASY OUTLINES: 

MATHEMATICAL HANDBOOK OF 

FORMULAS AND TABLES 

By Murray R Spiegel, Rensselaer Polytechnic Institute, and John Liu, 

Temple University 

2001 / 144 pages 

ISBN: 9780071369749 


CONTENTS 

Part 1: Formulas. 

Section 1: Elementary Constants, Products, Formulas. 

Section 2: Geometry. 

Section 3: Elementary Transcendental Functions. 

Section 4: Calculus. 

Section 5: Differential Equations. 

Section 6: Series. 

Section 7: Vector Analysis. 

Part 2: Tables. 

Section 8: Factorial n. 

Section 9: Conversion of Radians to Degrees, Minutes, and Seconds. 

Section 10: Conversion of Degrees, Minutes, and Seconds to Radians. 

Section 11: Sin x. 

Section 12: Cos x. 

Section 13: Tan x. 

Section 14: Natural or Naperian Logarithms log x or In x. 

Section 15: Exponential Functions e. 


HANDBOOK OF FORMULAS AND TABLES 

3rd Edition 

by Murray R. Spiegel (deceased), Seymour Lipschutz, Temple Universityphiladelphia, 

and John Liu, University of Maryland 


ISBN: 9780071548557 


This third edition covers elementary concepts in algebra, geometry, 

etc. and more advanced concepts in differential equations and vector 

analysis. It also expands its section on Probability and Statistics and 

includes a new section on Financial Mathematics to keep up with the 

 

math and the sciences. 

CONTENTS 

Formulas: 

1. Elementary Constants, Products, Formulas 

2. Geometry 

3. Elementary Transcendental Functions 

4. Calculus 

5. Differential Equations and Vector Analysis 

6. Series 

7. Special Functions and Polynomials 

8. Laplace and Fourier Transforms 

9. Elliptic and Miscellaneous Special Functions 

10. Inequalities and Infinite Products 



Tables: 

1. Logarithmic, Trigonometric, Exponential Functions 

2. Factorial and Gamma Function, Binomial Coefficients 

3. Bessel Functions 

4. Legendre Polynomials 

5. Elliptic Integrals 

Logic 

SCHAUM’S EASY OUTLINE OF LOGIC 

By John Nolt, University of Tennessee, Dennis Rohatyn, University of San 

Diego and Achille Varzi, Columbia University-New York 

2006 (September 2005) / 160pages 

ISBN: 9780071455350 


 

of Logic is perfect for anyone turned off by dense text. Cartoons, 

sidebars, icons, and other graphic pointers get the material across 

fast, and concise text focuses on the essence of logic. This is the 

ideal book for last-minute test preparation. 

126


Abstract Algebra 

SCHAUM’S OUTLINE OF ABSTRACT 

ALGEBRA 

2nd Edition 

by Lloyd R. Jaisingh, Morehead State University 

2004 / 288 pages 

ISBN: 9780071403276 


This long-awaited revision provides a concise introduction to topics 

in abstract algebra, taking full account of the major advances and 

developments that have occurred over the last half-century in the 

theoretical and conceptual aspects of the discipline, particularly in 

 

Integral Domains. 

Division Rings. 

Fields. 

Polynomials. 

Vector Spaces. 

Matrices. 

Matrix Polynomials. 

Linear Algebra. 


Topology 

Key features include: 

• A new section on binary linear codes 

• New chapter on Automorphisms and Galois Theory 

• 450 fully solved problems and 420 supplementary problems for 

individual practice 

• More than 175 illustrative examples 

SCHAUM’S OUTLINE OF GROUP THEORY 

By B Baumslag and B. Chandler, Ph.D., New York University 

1968 / 288 pages 

ISBN: 9780070041240 


CONTENTS 

Sets, Mappings and Binary Operations, Groupoids. 

Groups and Subgroups. 

Isomorphism Theorems. 

Finite Groups. 

Abelian Groups. 

Permutational Representations. 

Free Groups and Presentations. 

Appendices: A: Number Theory. 

B: Guide to the Literature. 

Symbols and Notations. 

SCHAUM’S OUTLINE OF GENERAL 

TOPOLOGY 


1986 / 256 pages 

ISBN: 9780070379886 


CONTENTS 

Sets and Relations. 

Functions. 

Cardinality, Order. 

Topology of the Line and Plane. 

Topological Spaces. 

Definitions. 

Bases and Subbases. 

Continuity and Topological Equivalence. 

Metric and Normed Spaces. 

Countability. 

Separation Axioms. 

Compactness. 

Product Spaces. 

Connectedness. 

Complete Metric Spaces. 

Function Spaces. 

Appendix. 

Properties of the Real Numbers. 

SCHAUM’S OUTLINE OF MODERN 

ABSTRACT ALGEBRA 

By Frank Ayres (deceased) 

1965 / 256 pages 

ISBN: 9780070026551 


CONTENTS 

Sets. 

Relations and Operations. 

The Natural Numbers. 

The Integers. 

Some Properties of Integers. 

The Rational Numbers. 

The Real Numbers. 

The Complex Numbers. 

Groups. 

Rings. 




 




127


128

Advanced Statistics ..........................................................................................140 


Applied Statistics - Education, Psychology and Social Science .......................136 

Applied Statistics - Engineering ........................................................................138 


Statistics and Probability (Calculus) .................................................................136 

Statistics and Probability (Non-Calculus) .........................................................131 



129

New Titles 



Elementary Statistics: A Step By Step Approach, 8e Bluman 9780077460396 131 



Statistics for Engineers and Scientists, 3e Navidi 9780073376332 138 

130


Statistics And Probability 

(Non-calculus) 


NEW *9780077460396* 

ELEMENTARY STATISTICS 

A Step By Step Approach, 

8th Edition 

by Allan G. Bluman, Cc Of Alleghney County 

South 

2012 (January 2011) / 896 pages 

ISBN: 9780077460396 

ISBN: 9780071317030 [IE] 

www.mhhe.com/bluman 

ELEMENTARY STATISTICS: A STEP BY STEP APPROACH is for 

introductory statistics courses with a basic algebra prerequisite. The 

book is non-theoretical, explaining concepts intuitively and teaching 

problem solving through worked examples and step-by-step instructions. 

In recent editions, Al Bluman has placed more emphasis on 

conceptual understanding and understanding results, along with 

increased focus on Excel, MINITAB, and the TI-83 Plus and TI-84 

Plus graphing calculators; computing technologies commonly used 

 

forward in terms of online course management with McGraw-Hill’s new 

homework platform, Connect Statistics – Hosted by ALEKS. Statistic 

instructors served as digital contributors to choose the problems that 

will be available, authoring each algorithm and providing stepped out 

solutions that go into great detail and are focused on areas where students 

commonly make mistakes. From there, the ALEKS Corporation 

reviewed each algorithm to ensure accuracy. The result is an online 

homework platform that provides superior content and feedback, allowing 



Connect Statistics – Hosted by ALEKS, McGraw-Hill’s new online 

homework platform provides accurate content developed by subject 

matter experts, with the ALEKS Corporation providing their expertise 

in ensuring the content is accurate. 

Chapter Summaries were updated into bulleted paragraphs 

representing each section from the chapter 

Over 250 new or updated exercises have been incorporated 

into the text. 

Over 30 new or updated examples have been incorporated into 

the text. 

FEATURES 

Critical Thinking Challenges - These problems extend the material 

in the chapter and are subsequently solved using the statistical 

techniques presented in the chapter. 

Procedure Tables - These boxes embody the text’s step by step 

approach and summarize methods for solving various types of common 

problems. Worked examples include every step. 

Speaking of Statistics - These sections invite students to think 

about poll results and other statistics-related news stories and apply 

what they have learned. 

Statistics Today - The outline and learning objectives of each 

chapter are followed by Statistics Today, a real-life problem that shows 

students the relevance of the chapter’s topic. 

Applying the Concepts – These exercises are found at the end 

of each section to reinforce concepts explained in the section. Most 

contain open-ended questions that require critical thinking and interpretation 

and may have more than one correct answer. 

At the end of appropriate sections, Technology Step by Step 

Boxes show students how to use MINITAB, the TI-83 Plus and TI-84 

Plus graphing calculators, and Excel to solve the types of problems 

covered in the section. 

Data Projects – Appear at the end of each chapter and often 

require students to gather, analyze and report on real data. They are 

specific to the areas of Business and Finance, Sports and Leisure, 

Technology, Health and Wellness, Politics and Economics, and the 

classroom. 

Technology Answers - The answers in the answer appendix now 

include solutions based on the use of tables as well as solutions with 

answers derived from technology (calculator, Minitab, Excel, etc.) 

when there are discrepancies. 

CONTENTS 

1 The Nature of Probability and Statistics 

2 Frequency Distributions and Graphs 

3 Data Description 

4 Probability and Counting Rules 

5 Discrete Probability Distributions 

6 The Normal Distribution 

7 Confidence Intervals and Sample Size 

8 Hypothesis Testing 

9 Testing the Difference Between Two Means, Two Variances, and 

Two Proportions 

10 Correlation and Regression 

11 Other Chi-Square Tests 

12 Analysis of Variance 

13 Nonparametric Statistics 

14 Sampling and Simulation 


Appendix B-1: Writing the Research Report 

Appendix B-2: Bayes’ Theorem 

Appendix B-3: Alternate Approach to the Standard Normal Distribution 

Appendix C: Tables 

Appendix D: Data Bank 

Appendix E: Glossary 

Appendix F: Bibliography 

Appendix G: Photo Credits 

Appendix H: Selected Answers 




 




131



ELEMENTARY STATISTICS 

A Brief Version, 5th Edition 

By Allan G Bluman, Community College of Allegheny County-South 

2010 (August 2009) 

ISBN: 9780077359423 

ISBN: 9780071220446 [IE, with CD and Formula Card] 


www.mhhe.com/bluman 

Elementary Statistics: A Brief Version, is a shorter version of the 

popular text Elementary Statistics: A Step by Step Approach. This 

softcover edition includes all the features of the longer book, but it is 

designed for a course in which the time available limits the number 

of topics covered. It is for general beginning statistics courses with 

a basic algebra prerequisite. The book is non-theoretical, explaining 

concepts intuitively and teaching problem solving through worked 

examples and step-by-step instructions. This edition places more 

emphasis on conceptual understanding and understanding results. 

This edition also features increased emphasis on Excel, MINITAB, 

and the TI-83 Plus and TI-84 Plus graphing calculators; computing 

technologies commonly used in such courses. 

CONTENTS 

1: The Nature of Probability and Statistics 

1.1 Descriptive and Inferential Statistics 

1.2 Variables and Types of Data 

1.3 Data Collection and Sampling Techniques 

1.4 Observational and Experimental Studies 

1.5 Uses and Misuses of Statistics 

1.6 Computers and Calculators 

2: Frequency Distributions and Graphs 

2.1 Organizing Data 

2.2 Histograms, Frequency Polygons, and Ogives 

2.3 Other Types of Graphs 

2.4 Paired Data and Scatter Plots 

3: Data Description 

3.1 Measures of Central Tendency 

3.2 Measures of Variation 

3.3 Measures of Position 

3.4 Exploratory Data Analysis 

4: Probability and Counting Rules 

4.1 Sample Spaces and Probability 

4.2 The Addition Rules for Probability 

4.3 The Multiplication Rules and Conditional Probability 

4.4 Counting Rules 

4.5 Probability and Counting Rules 

5: Discrete Probability Distributions 

5.1 Probability Distributions 

5.2 Mean, Variance, Standard Deviation, and Expectation 

5.3 The Binomial Distribution 

6: The Normal Distribution 

6.1 Normal Distributions 

6.2 Applications of the Normal Distribution 

6.3 The Central Limit Theorem 

6.4 The Normal Approximation to the Binomial Distribution 

7: Confidence Intervals and Sample Size 

7.1 Confidence Intervals for the Mean When É– Is Known and 

Sample Size 

7.2 Confidence Intervals for the Mean When É– Is Unknown 

7.3 Confidence Intervals and Sample Size for Proportions 

7.4 Confidence Intervals for Variances and Standard Deviations 

8: Hypothesis Testing 

8.1 Steps in Hypothesis Testing – Traditional Method 

8.2 z Test for a Mean 

8.3 t Test for a Mean 

8.4 z Test for a Proportion 

SCHAUM’S EASY OUTLINE OF STATISTICS 

2nd Edition 

By David P. Lindstrom and Murray R Spiegel (Deceased) 


ISBN: 9780071745819 


If you are looking for a quick nuts-and-bolts overview of statistics, it’s 


 

an emphasis on clarity and conciseness. Graphic elements such as 

sidebars, reader-alert icons, and boxed highlights stress selected 

points from the text, illuminate keys to learning, and give you quick 

pointers to the essentials. 



fields 


Topics include: Variables and Graphs, Measures of Central Tendency 

and Dispersion, Elementary Probability Theory, The Binomial, Normal, 

and Poisson Distributions, Elementary Sampling Theory, Statistical 

Estimation Theory, Statistical Decision Theory, Small Sampling 

Theory, The Chi-Square Test, Curve Fitting and the Method of Least 

Squares, Correlation Theory, Multiple and Partial Correlation, Analysis 

of Variation, Nonparametric Tests, Areas under the Standard Normal 

Curve, Student’s Distribution, Chi-Square Distribution, 99th Percentile 

Values for the F Distribution 

CONTENTS 

1. Variables and Graphs; 

2. Measures of Central Tendency and Dispersion; 

3. Elementary Probability Theory; 

4. The Binomial, Normal, and Poisson Distributions; 

5. Elementary Sampling Theory; 

6. Statistical Estimation Theory; 

7. Statistical Decision Theory; 

8. Small Sampling Theory; 

9. The Chi-Square Test; 

10. Curve Fitting and the Method of Least Squares; 

11. Correlation Theory; 

12. Multiple and Partial Correlation; 

13. Analysis of Variation; 

14. Nonparametric Tests; 

Appendix A: Areas under the Standard Normal Curve; 

Appendix B Student’s t Distribution; 

Appendix C: Chi-Square Distribution; 

Appendix D: 99th Percentile Values for the F Distribution; 

Index 

SCHAUM’S OUTLINE OF PROBABILITY 

2nd Edition 

By Seymour Lipschutz, Temple University and Marc Lipson, University of 

Georgia 


ISBN: 9780071755610 


Schaum’s Outline of Probability mirrors the course in scope and sequence 

to help enrolled students understand basic concepts and offer 

 

 

 

 

Stochastic and tree diagrams, Chebyshev’s Inequality and the Law 

of Large Numbers, calculations of binomial probabilities using the 

normal approximation, and regular Markov processes & stationary 

state distributions. 

132


CONTENTS 

1. Set Theory 

2. Techniques of Counting 

3. Introduction to Probability 

4. Conditional Probability and Independence 

5. Random Variables 

6. Binomial and Normal Distributions 

7. Markov Processes 

Appendix A: Descriptive Statistics 

Appendix B: Chi-Square Distribution 

SCHAUM’S OUTLINE OF STATISTICS 

4th Edition 

By Murray Spiegel and Larry Stephens 


ISBN: 9780071755498 


Schaum’s Outline of Statistics is a clear, readily understood review of 

the standard college statistics course for math and science majors, 

 

 

ing output from EXCEL, SAS, SPSS, STATISTIX, and MINITAB, all 

of which are now in general use for in college courses on statistics 

at this level. It also includes statistical examples taken from the latest 

media sources. 

CONTENTS 

1. Variables and Graphs 

2. Frequency Distributions 

3. The Mean, Median, Mode, and Other Measures of Central Tendency 

4. The Standard Deviation and Other Measures of Dispersion 

5. Moments, Skewness, and Kurtosis 

6. Elementary Probability Theory 

7. The Binomial, Normal, and Poisson Distributions 

8. Elementary Sampling Theory 

9. Statistical Estimation Theory 

10. Statistical Decision Theory 

11. Small Sampling Theory 

12. The Chi-Square Test 

13. Curve Fitting and the Method of Least Squares 

14. Correlation Theory 

15. Multiple Regression 

16. Analysis of Variance 

17. Nonparametric Tests 

18. Analysis of Time Series 

19. Statistical Process Control and Process Capability 

REVIEW COPY 











STATISTICS 

2nd Edition 

By Larry Stephens, University of Nebraska, Omaha 

2010 (August 2009) / 432 pages 

ISBN: 9780071635332 


This study tool is ideal if you wish to master the basics for an introductory 

course or solo study. This new edition includes output from Excel, 

SAS, SPSS, STATISTIX, and MINITAB, all of which are now in general 

use for college courses on statistics at this level. It will also include 

up-to-date statistical examples taken from the latest media sources. 

CONTENTS 

1. Introduction 

2. Organizing Data 

3. Descriptive Measures 


5. Discrete Random Variables 

6. Continuous Random Variables and Their Probability Distributions 

7. Sampling Distributions 

8. Estimation and Sample Size Determination: One Population 

9. Tests of Hypothesis: One Population 

10. Inferences for Two Populations 

11. Chi-Square Procedures 

SCHAUM’S OUTLINE OF BUSINESS 

STATISTICS 

2nd Edition 

By Larry Stephens, University of Nebraska, Omaha 

2010 (August 2009) / 416 pages 

ISBN: 9780071635271 


This study tool is ideal if you wish to master the basics for an introductory 

course or solo study. This new edition includes output from Excel, 

SAS, SPSS, STATISTIX, and MINITAB, all of which are now in general 

use for college courses on statistics at this level. It will also include 

up-to-date statistical examples taken from the latest media sources. 

CONTENTS 

1. Analyzing Business Data 

2. Statistical Presentations and Graphical Displays 

3. Describing Business Data: Measures of Location 

4. Describing Business Data: Measures of Dispersion 


6. Probability Distributions for Discrete Random Variables: Binomial, 

Hypergeometric, and Poission 

7. Probability Distributions for Continuous Random Variables: Normal 

and Exponential 

8. Sampling Distributions and Confidence Intervals for the Mean 

9. Other Confidence Intervals 

10. Testing Hypotheses Concerning the Value of a Population Mean 

11. Testing Other Hypotheses 

12. The Chi-Square Test for the Analysis of Qualitative Data 


14. Linear Regression and Correlation Analysis 

15. Multiple Regression and Correlation 

16. Time Series Analysis and Business Forecasting 

17. Nonparametric Statistics 

18. Decision Analysis: Payoff Tables and Decision Trees 

19. Statistical Process Control 

133


SCHAUM’S OUTLINE OF PROBABILITY AND 

STATISTICS 

3rd Edition 

by Murray R. Spiegel (deceased), John J. Schiller, R. Alu Srinivasan, 

Temple University 


ISBN: 9780071544252 


This Schaum’s Outline gives you 

 

Practice problems with full explanations that reinforce knowledge 

Coverage of the most up-to-date developments in your course 

field 

 

In-depth review of practices and applications 

Fully compatible with your classroom text, Schaum’s highlights all 

the important facts you need to know. Use Schaum’s to shorten your 

study time-and get your best test scores! 

CONTENTS 

Part I: Probability 

1. Basic Probability 

2. Random Variables and Probability Distributions 

3. Mathematical Expectation 

4. Special Probability Distributions 

Part II: Statistics 

5. Sampling Theory 

6. Estimation Theory 

7. Tests of Hypotheses and Significance 

8. Curve Fitting, Regression, and Correlation 



11. Bayesian Methods 

SCHAUM’S EASY OUTLINE OF BUSINESS 

STATISTICS 

By Leonard J. Kazmier, Arizona State University 

2003 / 160 pages 

ISBN: 9780071398763 


CONTENTS 

Chapter 1: Analyzing Business Data 

Chapter 2: Statistical Presentations and Graphical Analysis 

Chapter 3: Describing Business Data: Measures of Location 

Chapter 4: Describing Business Data: Measures of Variability 


Chapter 6: Probability Distributions for Discrete Random Variables 

Chapter 7: Probability Distributions for Continuous Random Variables 

Chapter 8: Sampling Distributions and Confidence Intervals for the 

Mean 

Chapter 9: Other Confidence Intervals 

Chapter 10: Testing Hypotheses Concerning the Value of the Population 

Mean 

Chapter 11: Testing Other Hypotheses 

Chapter 12: The Chi-Square Test 

Chapter 13: Analysis of Variance 

Chapter 14: Linear Regression and Correlation Analysis 

Chapter 15: Multiple Regression and Correlation 

Chapter 16: Time Series Analysis and Business Forecasting 

Chapter 17: Index Numbers for Business and Economic Data 

Chapter 18: Decision Analysis: Payoff Tables And Decision Trees 

Chapter 19: Decision Analysis: The Use of the Sample Information 

Chapter 20: Statistical Process Control 

Chapter 21: Nonparametric Statistics 

Appendices 

SCHAUM’S OUTLINE OF ELEMENTS OF 

STATISTICS II 

Inferential Statistics 

By Stephen Bernstein and Ruth Bernstein, University of Colorado 

2000 / 480 pages 

ISBN: 9780071346375 




STATISTICS I 

Differential Statistics and Probability 


1999 / 368 pages 

ISBN: 9780070050235 

ISBN: 9780071160599 [IE] - (Out-of-Print) 


CONTENTS 

Mathematics Required for Statistics. 

Characteristics of the Data. 

Populations, Samples, and Statistics. 

Descriptive Statistics: Organizing the Data Into Tables. 

Descriptive Statistics: Graphing the Data. 

Descriptive Statistics: Measures of Central Tendency, Average Value, 

and Location. 

Descriptive Statistics: Measures of Dispersion. 

Probability: The Classical, Relative Frequency, Set Theory, and 

Subjective Interpretations. 

Probability: Rules for Multiplication and Division, Marginal Probabilities 

and Bayes’ Theorem, Tree Diagrams and Counting Rules. 

Random Variables, Probability Distributions, Cumulative Distribution 

Functions, and Expected Values. 


PROBABILITY AND STATISTICS 

By Seymour Lipschutz and Jack Schiller, Temple University 

1998 / 384 pages 

ISBN: 9780070380844 


CONTENTS 

Part I: Descriptive Statistics and Probability. 

Preliminary: Descriptive Statistics. 

Sets and Counting. 

Basic Probability. 

Conditional Probability and Independence. 

Random Variables. 

Binomial and Normal Distributions. 

Part II: Inferential Statistics. 

Sampling Distributions. 

Confidence Intervals for A Single Population. 

Hypotheses Tests for A Single Population. 

Inference for Two Populations. 

Chi-Square Tests and Analysis of Variance. 

134



SCHAUM’S OUTLINE OF SET THEORY AND 

RELATED TOPICS 

2nd Edition 


1998 / 200 pages 

ISBN: 9780070381599 




CONTENTS 

Sets and Subsets. 

Basic Set Operators. 

Sets of Numbers. 

Functions. 

Product Sets and Graphs of Functions. 

Relations. 

Further Theory of Sets. 

Further Theory of Functions, Operations. 

Cardinal Numbers. 

Partially and Totally Ordered Sets. 

Well-Ordered Sets/Ordinal Numbers. 

Axiom of Choice. 

Paradoxes in Set Theory. 

Algebra of Propositions. 

Quantifiers. 


Logical Reasoning. 


STATISTICS FOR THE UTTERLY CONFUSED 

2nd Edition 

By Lloyd Jaisingh 

2006 / 352 pages 

ISBN: 9780071461931 


CONTENTS 

Part I: Descriptive Statistics 

1. Graphical Displays 

2. Numerical Measures of Central Tendency 

3. Numerical Measures of Variability 

4. Numerical Measures of Positions 

5. Exploring Bivariate Data 

6. Exploring Categorical Data 

Part II: Probability 

7. Randomness, Uncertainty, and Probability 

8. Discrete Probability Distributions 

9. The Normal Probability Distribution 

10. Sampling Distributions and the Central Limit Theorem 

Part III: Statistical Inference 

11. Confidence Intervals: Large Samples 

12. Hypothesis Tests: Large Samples 

13. Confidence Intervals and Hypothesis Tests: Small Samples 

14. Chi-Square Procedures 

15. One-Way Analysis of Variance 

PROBABILITY DEMYSTIFIED 

By Allan Bluman 

2005 / 258 pages 

ISBN: 9780071445498 


CONTENTS 

Chapter 1 – Basic Concepts of Probability 

Chapter 2 – Sample Spaces 

Chapter 3 – The Addition Rules 

Chapter 4 – The Multiplication Rules 

Chapter 5 – Odds and Expectation 

Chapter 6 – The Counting Rules 

Chapter 7 – The Binomial Distribution 

Chapter 8 – Other Probability Distributions 

Chapter 9 – The Normal Distribution 

Chapter 10– Simulation 

Final Exam 

Answers to Final Exam 

Appendix: Bayes’Theorem 

Index 

STATISTICS DEMYSTIFIED 


2004 / 355 pages 

ISBN: 9780071431187 


CONTENTS 

Preface 


PART 1: STATISTICAL CONCEPTS 

Chapter 1: Background Math 

Chapter 2: Learning the Jargon 

Chapter 3: Basics of Probability 

Chapter 4: Descriptive Measures 


PART 2: STATISTICS IN ACTION 

Chapter 5: Sampling and Estimation 

Chapter 6: Hypotheses, Prediction, and Regression 

Chapter 7: Correlation, Causation, Order, and Chaos 

Chapter 8: Some Practical Problems 


Final Exam 

Answers to Quiz, Test, and Exam Questions 


Index 

135


Statistics And Probability 

(Calculus) 

Applied Statistics – 

Education, Psychology and 

Social Science 


INTRODUCTION TO THE THEORY OF 

STATISTICS 

3rd Edition 

By Alexander M. Mood, University of California, Irvine Franklin A. Graybill, 

Duane C. Boes, both of Colorado State University 

1974 / 480 pages 


ISBN: 9780070854659 [IE] 

SCHAUM’S OUTLINE OF PROBABILITY AND 

STATISTICS 

3rd Edition 

By John J Schiller, R Alu Srinivasan, Temple University 

2009 (July 2008) / 399 pages 

ISBN: 9780071544252 




thousands of college and high school students who enroll in probability 

and statistics courses. 

CONTENTS 

Part I: Probability 

1. Basic Probability 

2. Random Variables and Probability Distributions 

3. Mathematical Expectation 

4. Special Probability Distributions 

Part II: Statistics 

5. Sampling Theory 

6. Estimation Theory 

7. Tests of Hypotheses and Significance 

8. Curve Fitting, Regression, and Correlation 



SPSS SURVIVAL MANUAL 

4th Edition 

By Julie Pallant, University of Melbourn 

2010 (November 2010) / 352 pages 

ISBN: 9780335242399 

(Open University Press) 

In this thoroughly revised edition of her bestselling text, now covering 

up to version 18 of the SPSS software, Julie Pallant guides you 

through the entire research process, helping you choose the right 

data analysis technique for your project. From the formulation of 

research questions, to the design of the study and analysis of data, 

to reporting the results, Julie discusses basic and advanced statistical 

techniques. She outlines each technique clearly, with easy to follow 

step-by-step procedures for performing the analysis, a detailed guide 

to interpreting data output and an example of how to present the results 

in a report. In this fourth edition all chapters have been updated 

to accommodate changes to SPSS procedures, screens and output. A 

number of additional techniques (McNemar’s Test, Cochran’s Q Test) 

have been included in the Non_parametric Statistics chapter. For both 

beginners and experienced users in psychology, sociology, health 

sciences, medicine, education, business and related disciplines, the 

SPSS Survival Manual is THE essential guide. Illustrated with screen 

grabs, examples of output and tips, it is supported by a website with 

sample data and guidelines on report writing. 

CONTENTS 

Preface 

Data files and website 

Introduction and overview 

Part One: Getting started 

Designing a study 

Preparing a codebook 

Getting to know SPSS 

Part Two: Preparing the data file 

Creating a data file and entering data 

Screening and cleaning the data 

Part Three: Preliminary analyses 

Descriptive statistics 

Using graphs to describe and explore the data 

Manipulating the data 

Checking the reliability of a scale 

Choosing the right statistic 

Part Four: Statistical techniques to explore relationships among 

variables 

Correlation 

Partial correlation 

Multiple regression 

Logistic regression 

Factor analysis 

Part Five: Statistical techniques to compare groups 

Non-parametric statistics 

T-tests 

One-way analysis of variance 

Two-way between-groups ANOVA 

Mixed between-within subjects analysis of variance 

Multivariate analysis of variance 

Analysis of covariance 

Appendix: Details of data files 

Recommended reading 

References 

Index 

136


BIOSTATISTICS FOR THE HEALTH 

SCIENCES 

by Karuthan Chinna, Krishnakumari Krishnan 


ISBN: 9789833850686 

(An Asian Publication) 

This book is an ideal introduction to the study of statistics applied 

 

 

 

background in statistics. 

CONTENTS 

Chapter 1: Introduction to Biostatistics 

Chapter 2: Descriptive Statistics 

Chapter 3: Statistical Distributions 

Chapter 4: Statistical Inference 

Chapter 5: One Sample Mean Test 

Chapter 6: Paired Sample Mean Test 

Chapter 7: Independent Samples Mean Test 

Chapter 8: One-Way ANOVA 

Chapter 9: One Sample Proportion Test 

Chapter 10: Two Samples Proportion Test 

Chapter 11: Contingency Tables 

Chapter 12: Bivariate Data Analysis 

Answers 

Appendix 

References 

STATISTICAL METHODS FOR CRIMINOLOGY 

AND CRIMINAL JUSTICE 

3rd Edition 

by Ronet Bachman, University Of Delaware, and Raymond Paternoster, 

University of Maryland---College Park 


ISBN: 9780073129242 

www.mhhe.com/bachman3e 

Statistical Methods for Criminology and Criminal Justice discusses 

the basic statistical procedures comprehensively while keeping it 

approachable and readable for students. Useful at both the introductory 

and intermediate levels, this text contains in-depth coverage of 

descriptive statistics, including graphical displays of data and exploratory 

data analysis, along with bivariate and multivariate analyses. 

Emphasis is placed equally on calculation and interpretation. The 

newly revised third edition offers new up-to-date crime data informa- 

 

crime, youth violence, hate crime and much more. 

CONTENTS 

Chapter 1: The Purpose of Statistics in the Criminological Sciences 

Chapter 2: Levels of Measurement and Aggregation 

Chapter 3: Understanding Data Distributions 

Chapter 4: Measures of Central Tendency 

Chapter 5: Measures of Dispersion 

Chapter 6: Probability, Probability Distributions, and an Introduction 

to Hypothesis Testing 

Chapter 7: Point Estimation and Confidence Intervals 

Chapter 8: From Estimation to Statistical Tests: Hypothesis Testing 

for one Population Mean and Proportion 

Chapter 9: Testing Hypotheses with Categorical Data 

Chapter 10: Hypothesis Tests Involving Two Population Means or 

Proportions 

Chapter 11: Hypothesis Tests Involving Three or More Population 

Means: Analysis of Variance 

Chapter 12: Bivariate Correlation and Regression 

Chapter 13: Controlling for a Third Variable: Multiple Regression and 

Partial Correlation 

Chapter 14: Regression Analysis with a Dichotomous Dependent 

Variable: Logit Models 

Appendix A: A Review of Basic Mathematical Operations 

Appendix B: Statistical Tables 

Appendix C: References 

THE STATA SURVIVAL GUIDE 

By David Pevalin and Karen Robson 

2009 (July 2009) / 392 pages 

ISBN: 9780335223886 

(Open University Press) 

• Where do I start? 

• How do I know if I’m asking the right questions? 

• How do I analyze the data once I have it? 

• How do I report the results? 

• When will I ever understand the process? 

If you are new to using the Stata software, and concerned about applying 

it to a project, help is at hand. David Pevalin and Karen Robson 

offer you a step by step introduction to the basics of the software, 

before gently helping you develop a more sophisticated understanding 

of Stata and its capabilities. 

The book will guide you through the research process offering further 

reading where more complex decisions need to be made and giving 

‘real world’ examples from a wide range of disciplines and anecdotes 

that clarify issues for readers. The book will help with: 

• Manipulating and organizing data 

• Generating statistics 

• Interpreting results 

• Presenting outputs 

The Stata Survival Manual is a lifesaver for both students and professionals 

who are using the Stata software! 

CONTENTS 

Introduction 

About the authors 

Acknowledgements 

Getting started with Stata 

Data in and out of Stata 

Manipulating variables 

Manipulating data 

Descriptive statistics and graphs 

Tables and correlations 

Differences in means, medians and proportions 

Regression 

Presenting your results 

References 

Index 

SCHAUM’S OUTLINE OF STATISTICS IN 

PSYCHOLOGY 

by Larry J. Stephens, University of Nebraska, Omaha 


ISBN: 9780071545990 


Schaum’s Outline of Statistics in Psychology helps students to understand 

basic concepts and offers extra practice on such topics as 

frequency distributions, central tendency, inferential statistics, probability 

and samples, z scores, the t-Test, correlations, and nonparametric 

tests. Coverage will also include the design of experiments and 

surveys, their execution, and the statistical tasks required to make 

sense of the date obtained using these techniques. A special section 

on computer-use for particular statistical tasks has also been included. 

137



STATISTICS II 

Inferential Statistics 


2000 / 480 pages 

ISBN: 9780071346375 




STATISTICS I 

Differential Statistics and Probability 


1999 / 368 pages 

ISBN: 9780070050235 



CONTENTS 

Mathematics Required for Statistics. 

Characteristics of the Data. 

Populations, Samples, and Statistics. 

Descriptive Statistics: Organizing the Data Into Tables. 

Descriptive Statistics: Graphing the Data. 

Descriptive Statistics: Measures of Central Tendency, Average Value, 

and Location. 

Descriptive Statistics: Measures of Dispersion. 

Probability: The Classical, Relative Frequency, Set Theory, and 

Subjective Interpretations. 

Probability: Rules for Multiplication and Division, Marginal Probabilities 

and Bayes’ Theorem, Tree Diagrams and Counting Rules. 

Random Variables, Probability Distributions, Cumulative Distribution 

Functions, and Expected Values. 

Applied Statistics - 

Engineering 


NEW *9780073376332* 

STATISTICS FOR 

ENGINEERS AND 

SCIENTISTS 

3rd Edition 

by William Navidi, Colorado School Of Mines 


ISBN: 9780073376332 

ISBN: 9780071222051 [IE] 

www.mhhe.com/navidi 

Statistics for Engineers and Scientists stands out for its crystal clear 

presentation of applied statistics. Suitable for a one or two semester 

course, the book takes a practical approach to methods of statistical 

 

Statistics for Engineers and Scientists features a unique approach 

 

clearly, along with the use of contemporary real world data sets to 

help motivate students and show direct connections to industry and 

research. While focusing on practical applications of statistics, the text 

makes extensive use of examples to motivate fundamental concepts 

and to develop intuition. 


 

Over 250 new problems have been added 

A new section was added on Tolerance and Prediction Intervals 

in Chapter 5; the discussion of controlled experiments and observational 

studies was added to Chapter 1; and confounding in controlled 

experiments was added in Chapter 7. 

A CONNECT site features power points, Datasets, image library, 

solutions, and algorithmic problems. 

REVIEW COPY 










CONTENTS 

Chapter 1: Sampling and Descriptive Statistics 


Chapter 3: Propagation of Error 

Chapter 4: Commonly Used Distributions 

Chapter 5: Confidence Intervals 

Chapter 6: Hypothesis Testing 

Chapter 7: Correlation and Simple Linear Regression 

Chapter 8: Multiple Regression 

Chapter 9: Factorial Experiments 

Chapter 10: Statistical Quality Control 

A Tables 

B Partial Derivatives 

C Suggestions for Further Reading 


138



PRINCIPLES OF STATISTICS FOR 

ENGINEERS AND SCIENTISTS 

by William C. Navidi, Colorado School Of Mines 


ISBN: 9780077289317 

ISBN: 9780070166974 [IE] 

www.mhhe.com/navidi 

Principles of Statistics for Engineers and Scientists offers the same 

crystal clear presentation of applied statistics as Bill Navidi’s Statistics 

for Engineers and Scientists text, in a manner especially designed 

for the needs of a one-semester course that focuses on applications. 

The text features a unique approach accentuated by an engaging 

writing style that explains difficult concepts clearly. By presenting 

ideas in the context of real-world data featured in plentiful examples, 

the book motivates students to understand fundamental concepts 

through practical examples found in industry and research. 

CONTENTS 

1 Sampling and Descriptive Statistics 

2 Summarizing Bivariate Data 

3 Probability 

4 Commonly Used Distributions 

5 Point and Interval Estimation for a Single Sample 

6 Hypothesis Tests for a Single Sample 

7 Inferences for Two Samples 

8 Inference in Linear Models 

9 Factorial Experiments 

10 Statistical Quality Control 


INTRODUCTION TO PROBABILITY AND 

STATISTICS 

Principles and Applications for Engineering and 

the Computing Sciences, 4th Edition 

By J Susan Milton, Emeritus, Radford University and Jesse C Arnold, 

Virginia Polytechnic Institute 

2003 / 816 pages 

ISBN: 9780072468366 

ISBN: 9780071242486 [IE, 2-colour Text] 

ISBN: 9780071198592 [IE] 

www.mhhe.com/miltonarnold 

CONTENTS 

1 Introduction to Probability and Counting: 

Interpreting Probabilities. 

Sample Spaces and Events. 

Permutations and Combinations. 

2 Some Probability Laws. 

Axioms of Probability. 

Conditional Probability. 

Independence and the Multiplication Rule. 

Bayes’ Theorem. 

3 Discrete Distributions. 

Random Variables. 

Discrete Probablility Densities. 

Expectation and Distribution Parameters. 

Geometric Distribution and the Moment Generating Function. 

Binomial Distribution. 

Negative Binomial Distribution. 

Hypergeometric Distribution. 

Poisson Distribution. 

4 Continuous Distributions. 

Con-tinuous Densities. 

Expectation and Distribution Parameters. 

Gamma Distribution. 

Normal Distri-bution. 

Normal Probability Rule and Chebyshev’s Inequality. 

Normal Approximation to the Binomial Distribution. 

Weibull Distribution and Reliability. 

Transformation of Variables. 

Simulating a Continuous Distribution. 

5 Joint Distributions. 

Joint Densities and Independence. 

Expectation and Covariance. 

Correlation. 

Conditional Densities and Regression. 

Transformation of Variables. 

6 Descriptive Statistics. 

Random Sampling. 

Picturing the Distribution. 

Sample Statistics. 

Boxplots. 

7 Estimation. 

Point Estimation. 

The Method of Moments and Maximum Likelihood. 

Functions of Random Variables - Distribution of X. 

Interval Estimation and the Central Limit Theorem. 

8 Inferences on the Mean and Variance of a Distribution. 

Interval Estimation of Variability. 

Estimating the Mean and the Student-t Distribution. 

Hypothesis Testing. 

Significance Testing. 

Hypothesis and Significance Tests on the Mean. 

Hypothesis Tests. 

Alternative Nonparametric Methods. 

9 Inferences on Proportions. 

Estimating Proportions. 

Testing Hypothesis on a Proportion. 

Comparing Two Proportions: Estimation. 

Coparing Two Proportions: Hypothesis Testing. 

10 Comparing Two Means and Two Variances. 

Point Estimation. 

Comparing Variances: The F Distribution. 

Comparing Means: Variances Equal (Pooled Test). 

Comparing Means: Variances Unequal. 

Compairing Means: Paried Data. 


A Note on Technology. 

11 Sample Linear Regression and Correlation. 

Model and Parameter Estimation. 

Properties of Least-Squares Estimators. 

Confidence Interval Estimation and Hypothesis Testing. 

Repeated Measurements and Lack of Fit. 

Residual Analysis. 

Correlation. 

12 Multiple Linear Regression Models. 

Least-Squares Procedures for Model Fitting. 

A Matrix Approach to Least Squares. 

Properties of the Least-Squares Estimators. 

Interval Estimation. 

Testing Hypotheses about Model Parameters. 

Use of Indicator or “Dummy” Variables. 

Criteria for Variable Selection. 

Model Transformation and Concluding Remarks. 

13 Analysis of Variance. 

One-Way Classification Fixed-Effects Model. 

Comparing Variances. 

Pairwise Comparison. 

Testing Contrasts. 

Randomized Complete Block Design. 

139


Latin Squares. 

Random-Effects Models. 

Design Models in Matrix Form. 


14 Factorial Experiments. 

Two-Factor Analysis of Variance. 

Extension to Three Factors. 

Random and Mixed Model Factorial Experiments. 

2^k Factorial Experiments. 

2^k Factorial Experiments in an Incomplete Block Design. 

Fractional Factorial Experiments. 

15 Categorical Data. 

Multinomial Distribution. 

Chi-Squared Goodness of Fit Tests. 

Testing for Independence. 

Comparing Proportions. 

16 Statistical Quality Control. 

Properties of Control Charts. 

Shewart Control Charts for Measurements. 

Shewart Control Charts for Attributes. 

Tolerance Limits. 

Acceptance Sampling. 

Two-Stage Acceptance Sampling. 

Extensions in Quality Control. 

Appendix A Statistical Tables. 

Appendix B Answers to Selected Problems. 

Appendix C Selected Derivations 

MULTIVARIATE STATISTICAL METHODS IN 

QUALITY MANAGEMENT 

By Kai Yang and Jayant Trewn 

2004 / 299 pages 

ISBN: 9780071432085 


CONTENTS 

Chapter 1: Multivariate Statistical Methods and Quality 

Chapter 2: Graphical Multivariate Data Display and Data Stratification 

Chapter 3: Introduction to Multivariate Random Variables, Normal 

Distribution, and Sampling Properties 

Chapter 4: Multivariate Analysis of Variance 

Chapter 5: Principal Component Analysis and Factor Analysis 

Chapter 6: Discriminant Analysis 

Chapter 7: Cluster Analysis 

Chapter 8: Mahalanobis Distance and Taguchi Method 

Chapter 9: Path Analysis and the Structural Method 

Chapter 10: Multivariate Statistical Process Control 

APPENDIX: PROBABILITY DISTRIBUTION TABLES 

REFERENCES 

INDEX 

Advanced Statistics 


ENGINEERING STATISTICS DEMYSTIFIED 

By Larry Stephens, University of Nebraska 

2007 / 448 pages 

ISBN: 9780071462723 


CONTENTS 

Preface 


Chapter 1: Treatment of Data Using EXCEL, MINITAB, SAS, SPSS, 

and STATISTIX 


Chapter 3: Probability Distributions for Discrete Random Variables 

Chapter 4: Probability Densities for Continuous Random Variables 

and Introduction to MAPLE 

Chapter 5: Sampling Distributions 

Chapter 6: Inferences Concerning Means 

Chapter 7: Inferences Concerning Variances 

Chapter 8: Inferences Concerning Proportions 

FINAL EXAMINATIONS 

SOLUTIONS TO CHAPTER EXERCISES 

BIBLIOGRAPHY 

INDEX 


APPLIED LINEAR STATISTICAL MODELS 

5th Edition 

By Michael H Kutner, Emory University; Christopher J Nachtsheim, 

University of Minnesota; John Neter, University of Georgia and William 

Li, University of Minnesota 

2005 / 1,200 pages 

ISBN: 9780073108742 (with CD) 

ISBN: 9780071122214 [IE with CD] 

CONTENTS 

Part 1 Simple Linear Regression: 

1 Linear Regression with One Predictor Variable. 

2 Inferences in Regression and Correlation Analysis. 

3 Diagnostic and Remedial Measures. 

4 Simultaneous Inferences and Other Topics in Regression Analysis. 

5 Matrix Approach to Simple Linear Regression Analysis. 

Part 2 Multiple Linear Regression: 

6 Multiple Regression I. 

7 Multiple Regression II. 

8 Regression Models for Quantitative and Qualitative Predictors. 

9 Building the Regression Model I: Model Selection and Validation. 

10 Building the Regression Model II: Diagnostics. 

11 Building the Regression Model III: Remedial Measures. 

12 Autocorrelation in Time Series Data. 

Part 3 Nonlinear Regression: 

13 Introduction to Nonlinear Regression and Neural Networks. 

14 Logistic Regression, Poisson Regression, and Generalized Linear 

Models. 

Part 4 Design and Analysis of Single-Factor Studies: 

15 Introduction to the Design of Experimental and Observational 

Studies. 

16 Single Factor Studies. 

17 Analysis of Factor-Level Means. 

18 ANOVA Diagnostics and Remedial Measures. 

Part 5 Multi-Factor Studies: 

140


19 Two Factor Studies with Equal Sample Sizes. 

20 Two Factor Studies-One Case per Treatment. 

21 Randomized Complete Block Designs. 

22 Analysis of Covariance. 

23 Two Factor Studies with Unequal Sample Sizes. 

24 MultiFactor Studies. 

25 Random and Mixed Effects Models. 

Part 6 Specialized Study Designs: 

26 Nested Designs, Subsampling, and Partially Nested Designs. 

27 Repeated Measures and Related Designs. 

28 Balanced Incomplete Block, Latin Square, and Related Designs. 

29 Exploratory Experiments: Two-Level Factorial and Fractional 

Factorial Designs. 

30 Response Surface Methodology. 

Appendix A: Some Basic Results in Probability and Statistics. 

Appendix B: Tables. 

Appendix C: Data Sets. 

Appendix D: Rules for Develping ANOVA Models and Tables for 

Balanced Designs. 

Appendix E: Selected Bibliography 

SCHAUM’S OUTLINE OF STATISTICS 

4th Edition 

By Murray Spiegel (deceased) and Larry J Stephens, University of Nebraska, 

Omaha 


ISBN: 9780071755498 


Schaum’s Outline of Statistics is a clear, readily understood review of 

the standard college statistics course for math and science majors, 

 

 

ing output from EXCEL, SAS, SPSS, STATISTIX, and MINITAB, all 

of which are now in general use for in college courses on statistics 

at this level. It also includes statistical examples taken from the latest 

media sources. 

CONTENTS 

1. Variables and Graphs 

2. Frequency Distributions 

3. The Mean, Median, Mode, and Other Measures of Central Tendency 

4. The Standard Deviation and Other Measures of Dispersion 

5. Moments, Skewness, and Kurtosis 

6. Elementary Probability Theory 

7. The Binomial, Normal, and Poisson Distributions 

8. Elementary Sampling Theory 

9. Statistical Estimation Theory 

10. Statistical Decision Theory 

11. Small Sampling Theory 

12. The Chi-Square Test 

13. Curve Fitting and the Method of Least Squares 

14. Correlation Theory 

15. Multiple Regression 



18. Analysis of Time Series 

19. Statistical Process Control and Process Capability 


ADVANCED STATISTICS DEMYSTIFIED 

By Larry Stephens, University of Nebraska 

2004 / 324 pages 

ISBN: 9780071432429 


CONTENTS 

Preface 

Introduction: A Review of Inferences Based on a Single Sample 

Chapter 1: Inferences Based on Two Samples 

Chapter 2: Analysis of Variance: Comparing More Than Two Means 

Chapter 3: Simple Linear Regression and Correlation 

Chapter 4: Multiple Regression 

Chapter 5: Nonparametric Statistics 

Chapter 6: Chi-Squared Tests 

Final Exams and Their Answers 

Solutions to Chapter Exercises 

Bibliography 

Index 




 




141


142

A 

Title Index 

Advanced Statistics Demystified Stephens 141 

Algebra & Trigonometry, 2e Coburn 66 

Algebra for College Students, 6e Dugopolski 37 

Applied and Algorithmic Graph Theory Chartrand 118 

Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition, 10e Hoffmann 79 

Applied Linear Statistical Models, 5e Kutner 140 

Applied Mathematics for Business, Economics and the Social Science, 4e Budnick 45 

Arithmetic and Algebra Again, 2e Immergut 6, 10, 18 

B 

Basic College Mathematics, 2e Miller 4 

Basic College Mathematics, 4e Bello 3 

Beginning Algebra Messersmith 12 

Beginning Algebra, 3e Miller 14 

Beginning and Intermediate Algebra, 3e Messersmith 21 

Beginning and Intermediate Algebra, 3e Miller 25 

Beginning and Intermediate Algebra: The Language and Symbolism of Mathematics, 3e Hall 24 

Biostatistics for the Health Sciences Chinna 137 

Bob Miller’s Algebra for the Clueless, 2e Miller 18 

Bob Miller’s Calc for the Clueless: Calc I, 2e Miller 87, 93 

Bob Miller’s Calc for the Clueless: PreCalc, 3e Miller 75 

Business Calculus Demystified Huettenmueller 80 

Business Math Demystified Bluman 54 

C 

Calculus for Business, Economics, and the Social and Life Sciences, Brief Edition, 10e Hoffmann 79 

Calculus with Analytic Geometry, 2e Simmons 84 

Calculus, 4e Smith 81 

Calculus, Single Variable: Late Transcendental Functions, 3e Smith 88 

Calculus: Concepts and Connections Smith 83 

Calculus: Early Transcendental Functions, 4e Smith 82, 87, 93 

Calculus: Multivariable: Early Transcendental Functions, 3e Smith 96 

Calculus: Multivariable: Late Transcendental Functions, 3e Smith 94 

Calculus: Single Variable: Early Transcendental Functions, 3e Smith 90 

College Algebra Demystified Huettenmueller 62 

College Algebra Essentials, 2e Coburn 60 

College Algebra with Trigonometry, 9e Barnett 64 

College Algebra, 2e Coburn 59 

College Algebra, 9e Barnett 58 

College Algebra: Graphs and Models Coburn 57 

College Algebra: Graphs and Models, 3e Barnett 61 

Complex Analysis, 3e Ahlfors 123 

Complex Variables and Applications, 8e Brown 121 

Complex Variables Demystified McMahon 124 

143

D 

Title Index 

Differential Equations Ang 102 

Differential Equations Demystified Krantz 103, 105 

Differential Equations with Applications and Historical Notes, 2e Simmons 103 

Differential Equations: A Modeling Approach Ledder 102 

Differential Equations: Theory, Technique, and Practice Simmons 101, 104 

Discrete Mathematics and Its Applications, 7e Rosen 48 

E 

Elementary Algebra, 6e Dugopolski 16 

Elementary and Intermediate Algebra, 4e Dugopolski 19 

Elementary and Intermediate Algebra: Alternate Hardcover Edition, 3e Hutchinson 27 

Elementary Linear Algebra, 2e Nicholson 112 

Elementary Number Theory, 7e Burton 120 

Elementary Numerical Analysis: An Algorithmic Approach, 3e Conte 120 

Elementary Statistics: A Brief Version, 5e Bluman 132 

Elementary Statistics: A Step By Step Approach, 8e Bluman 131 

Engineering Statistics Demystified Stephens 140 

Everyday Math Demystified Gibilisco 6 

F 

Five Steps to a 5 AP Calculus AB and BC, 3e Ma 98 

Fourier Series and Boundary Value Problems, 7e Brown 107 

Fourier Series and Boundary Value Problems, 8e Brown 106 

Functional Analysis, 2e Rudin 124 

G 

Geometry Demystified Gibilisco 44 

H 

Higher Engineering Mathematics Ramana 116 

History of Mathematics: An Introduction, 7e (The) Burton 119 

How to solve Math Word Problems on Standardized Tests Wayne 6, 10, 18 

How to Solve Word Problems in Calculus Don 87, 93, 98 

How to solve Word Problems in Mathematics Wayne 7, 11, 19 

Hutchinson’s Basic Mathematical Skills with Geometry, 8e Baratto 4 

Hutchinson’s Beginning Algebra, 8e Baratto 15 

Hutchinson’s Elementary and Intermediate Algebra, 4e Baratto 23 

144

I 

Title Index 

Intermediate Algeba, 7e Dugopolski 29 

Intermediate Algebra Messersmith 31 

Intermediate Algebra Hutchinson 35 

Intermediate Algebra, 2e Miller 34 

Intermediate Algebra, 3e Miller 32 

Intermediate Algebra, 3e Bello 34 

Introduction to Enumerative Combinatorics Bona 108, 114 

Introduction to Graph Theory Chartrand 109, 117 

Introduction to Linear Algebra DeFranza 111 

Introduction to Probability and Statistics: Principles and Applications for Engineering and the Milton 139 

Computing Sciences, 4e 

Introduction to the Theory of Statistics, 3e Mood 136 

Introductory Algebra, 2e Miller 15 

Introductory Algebra, 4e Bello 11 

L 

Linear Algebra Demystified McMahon 114 

Linear Algebra with Applications, 6e Nicholson 112 

M 

Mastering Technical Mathematics, 3e Gibilisco 51 

Math Proofs Demystified Gibilisco 111 

Math Word Problems Demystified Bluman 6, 10, 18, 28, 36, 40 

Mathcad: A Tool for Engineers and Scientists (B.E.S.T. Series), 2e Pritchard 115 

Mathematics for Elementary Teachers: A Conceptual Approach, 9e Bennett 46 

Mathematics for Elementary Teachers: An Activity Approach, 9e Bennett 47 

Mathematics for Technicians, 6e Alldis 50 

Mathematics in Our World, 2e Sobecki 44 

Miller’s Geometry for the Clueless, 2e Miller 43 

Multivariate Statistical Methods in Quality Management Yang 140 

P 

Prealgebra Miller 7 

Prealgebra, 2e Hutchison 9 

Prealgebra: Media Enhanced Edition, 3e Baratto 8 

Pre-Calculus Demystified Huettenmueller 74 

Precalculus with Limits, 6e Barnett 72 

Precalculus, 2e Coburn 70 

Precalculus, 7e Barnett 69 

Precalculus: Graphs & Models Coburn 67 

Precalculus: Graphs & Models, 3e Barnett 71 

Principles of Mathematical Analysis, 3e Rudin 110, 118 

Principles of Statistics for Engineers and Scientists Navidi 139 

Probability Demystified Bluman 135 

145

R 

Title Index 

Real and Complex Analysis, 3e Rudin 109, 123, 125 

S 

Schaum’s 2,000 Solved Problems in Discrete Mathematics Lipschutz 49 

Schaum’s 3,000 Solved Problems in Calculus Mendelson 92 

Schaum’s 3,000 Solved Problems in Linear Algebra Lipschutz 113 

Schaum’s A-Z Mathematics Berry 5 

Schaum’s Easy Outline Intermediate Algebra Steege 37 

Schaum’s Easy Outline of Business Statistics Kazmier 134 

Schaum’s Easy Outline of Calculus, 2e Mendenson 91 

Schaum’s Easy Outline of College Algebra, 2e Moyer 62 

Schaum’s Easy Outline of College Mathematics Ayres 53 

Schaum’s Easy Outline of Differential Equations Bronson 105 

Schaum’s Easy Outline of Introduction to Mathematical Economics Dowling 54 

Schaum’s Easy Outline of Logic Nolt 126 

Schaum’s Easy Outline of Statistics, 2e Lindstrom 132 

Schaum’s Easy Outlines: Geometry, 2e Rich 43 

Schaum’s Easy Outlines: Linear Algebra Lipschutz 113 

Schaum’s Easy Outlines: Mathematical Handbook of Formulas and Tables Spiegel 126 

Schaum’s Outline of Abstract Algebra, 2e Jaisingh 127 

Schaum’s Outline of Advanced Calculus, 3e Wrede 86, 119 

Schaum’s Outline of Advanced Mathematics for Engineers and Scientists Spiegel 117 

Schaum’s Outline of Basic Business Mathematics, 2e Don 51 

Schaum’s Outline of Basic Mathematics for Electricity and Electronics Beiser 53 

Schaum’s Outline of Basic Mathematics with Applications to Science and Technology, 2e Kruglak 51 

Schaum’s Outline of Beginning Calculus, 3e Mendelson 73, 92 

Schaum’s Outline of Beginning Finite Mathematics Lipschutz 52, 53 

Schaum’s Outline of Beginning Linear Algebra Lipschutz 113 

Schaum’s Outline of Beginning Statistics, 2e Stephens 133 

Schaum’s Outline of Boolean Algebra and Switching Circuits Mendelson 49 

Schaum’s Outline of Business Statistics, 2e Stephens 133 

Schaum’s Outline of Calculus for Business, Economics, and the Social Sciences Dowling 80 

Schaum’s Outline of Calculus of Finite Differences and Difference Equations Spiegel 119 

Schaum’s Outline of Calculus, 5e Ayres 86, 91, 97 

Schaum’s Outline of College Algebra, 3e Spiegel 39 

Schaum’s Outline of College Algebra, 3e Moyer 62 

Schaum’s Outline of Combinatorics Balakrishnan 115 

Schaum’s Outline of Complex Variables, 2e Spiegel 124 

Schaum’s Outline of Differential and Integral Calculus, SI Metric, 3e Ayres 92 

Schaum’s Outline of Differential Equations, 3e Bronson 103, 105 

Schaum’s Outline of Differential Geometry Lipschutz 121 

Schaum’s Outline of Discrete Mathematics, Revised 3e Lipschutz 49 

Schaum’s Outline of Elementary Algebra, 3e Rich 17 

Schaum’s Outline of Elements of Statistics I: Differential Statistics and Probability Bernstein 134, 138 

146

Title Index 

Schaum’s Outline of Elements of Statistics II: Inferential Statistics Bernstein 134, 138 

Schaum’s Outline of Fourier Analysis with Applications to Boundary Value Problems Spiegel 107 

Schaum’s Outline of General Topology Lipschutz 127 

Schaum’s Outline of Geometry, 4e Rich 43 

Schaum’s Outline of Graph Theory: Including Hundreds of Solved Problems Balakrishnan 118 

Schaum’s Outline of Group Theory Baumslag 127 

Schaum’s Outline of Intermediate Algebra, 2e Steege 36 

Schaum’s Outline of Introduction to Mathematical Economics, 3e Dowling 52, 54 

Schaum’s Outline of Introduction to Mathematical Economics, Revised 3e Dowling 50 

Schaum’s Outline of Introduction to Probability and Statistics Lipschutz 134 

Schaum’s Outline of Laplace Transforms Spiegel 103, 105, 107 

Schaum’s Outline of Linear Algebra, 4e Lipschutz 113 

Schaum’s Outline of Mathematica, 2e Don 92, 97 

Schaum’s Outline of Mathematical Handbook of Formulas and Tables, 3e Spiegel 39, 126 

Schaum’s Outline of Mathematical Methods for Business and Economics Dowling 50 

Schaum’s Outline of Mathematics for Liberal Arts Majors Thomas 45 

Schaum’s Outline of Mathematics for Nurses Stephens 52 

Schaum’s Outline of Mathematics of Finance, 2e Zima 54 

Schaum’s Outline of Modern Abstract Algebra Ayres 127 

Schaum’s Outline of Numerical Analysis, 2e Scheid 120 

Schaum’s Outline of Partial Differential Equations DuChateau 107 

Schaum’s Outline of Precalculus, 2e Safier 74 

Schaum’s Outline of Probability and Statistics, 2e Spiegel 134 

Schaum’s Outline of Probability and Statistics, 3e Schiller 136 

Schaum’s Outline of Probability, 2e Lipschutz 132 

Schaum’s Outline of Review of Elementary Mathematics, 2e Rich 5 

Schaum’s Outline of Set Theory and Related Topics, 2e Lipschutz 135 

Schaum’s Outline of Statistics in Psychology Stephens 137 

Schaum’s Outline of Statistics, 4e Spiegel 133, 141 

Schaum’s Outline of Tensor Calculus Kay 116, 117 

Schaum’s Outline of Trigonometry, 4e Moyer 64 

Solving Business Problems Using a Calculator Student Text, 6e Polisky 53 

Spreadsheet Tools for Engineers Using Excel, 3e Gottfried 116 

SPSS Survival Manual, 4e Pallant 136 

Stata Survival Guide (The) Pevalin 137 

Statistical Methods for Criminology and Criminal Justice, 3e Bachman 137 

Statistics Demystified Gibilisco 135 

Statistics for Engineers and Scientists, 3e Navidi 138 

Statistics for the Utterly Confused, 2e Jaisingh 135 

Supersymmetry Demystified LaBelle 51 

147

T 

Title Index 

Teach Yourself Algebra, 2e Abbott 29, 37, 40 

Teach Yourself Trigonometry, 2e Abbott 64 

Technical Math Demystified Gibilisco 52 

Test Yourself: Elementary Algebra Trivieri 19 

Test Yourself: Intermediate Algebra Van Glabek 37 

Transition to Higher Mathematics: Structure and Proof Dumas 108, 110 

Trigonometry Demystified Gibilisco 64 

Trigonometry, 2e Coburn 62 

148

A 

Author Index 

Abbott Teach Yourself Algebra, 2e 29, 37, 40 

Abbott Teach Yourself Trigonometry, 2e 64 

Ahlfors Complex Analysis, 3e 123 

Alldis Mathematics for Technicians, 6e 50 

Ang Differential Equations 102 

Ayres Schaum’s Easy Outline of College Mathematics 53 

Ayres Schaum’s Outline of Calculus, 5e 86, 91, 97 

Ayres Schaum’s Outline of Differential and Integral Calculus, SI Metric, 3e 92 

Ayres Schaum’s Outline of Modern Abstract Algebra 127 

B 

Bachman Statistical Methods for Criminology and Criminal Justice, 3e 137 

Balakrishnan Schaum’s Outline of Combinatorics 115 

Balakrishnan Schaum’s Outline of Graph Theory: Including Hundreds of Solved Problems 118 

Baratto Hutchinson’s Basic Mathematical Skills with Geometry, 8e 4 

Baratto Hutchinson’s Beginning Algebra, 8e 15 

Baratto Hutchinson’s Elementary and Intermediate Algebra, 4e 23 

Baratto Prealgebra: Media Enhanced Edition, 3e 8 

Barnett College Algebra with Trigonometry, 9e 64 

Barnett College Algebra, 9e 58 

Barnett College Algebra: Graphs and Models, 3e 61 

Barnett Precalculus with Limits, 6e 72 

Barnett Precalculus, 7e 69 

Barnett Precalculus: Graphs & Models, 3e 71 

Baumslag Schaum’s Outline of Group Theory 127 

Beiser Schaum’s Outline of Basic Mathematics for Electricity and Electronics 53 

Bello Basic College Mathematics, 4e 3 

Bello Intermediate Algebra, 3e 34 

Bello Introductory Algebra, 4e 11 

Bennett Mathematics for Elementary Teachers: A Conceptual Approach, 9e 46 

Bennett Mathematics for Elementary Teachers: An Activity Approach, 9e 47 

Bernstein Schaum’s Outline of Elements of Statistics I: Differential Statistics and Probability 134, 138 

Bernstein Schaum’s Outline of Elements of Statistics II: Inferential Statistics 134, 138 

Berry Schaum’s A-Z Mathematics 5 

Bluman Business Math Demystified 54 

Bluman Elementary Statistics: A Brief Version, 5e 132 

Bluman Elementary Statistics: A Step By Step Approach, 8e 131 

Bluman Math Word Problems Demystified 6, 10, 18, 28, 36, 40 

Bluman Probability Demystified 135 

Bona Introduction to Enumerative Combinatorics 108, 114 

Bronson Schaum’s Easy Outline of Differential Equations 105 

Bronson Schaum’s Outline of Differential Equations, 3e 103, 105 

Brown Complex Variables and Applications, 8e 121 

Brown Fourier Series and Boundary Value Problems, 7e 107 

149

Author Index 

Brown Fourier Series and Boundary Value Problems, 8e 106 

Budnick Applied Mathematics for Business, Economics and the Social Science, 4e 45 

Burton Elementary Number Theory, 7e 120 

Burton History of Mathematics: An Introduction, 7e (The) 119 

C 

Chartrand Applied and Algorithmic Graph Theory 118 

Chartrand Introduction to Graph Theory 109, 117 

Chinna Biostatistics for the Health Sciences 137 

Coburn Algebra & Trigonometry, 2e 66 

Coburn College Algebra Essentials, 2e 60 

Coburn College Algebra, 2e 59 

Coburn College Algebra: Graphs and Models 57 

Coburn Precalculus, 2e 70 

Coburn Precalculus: Graphs & Models 67 

Coburn Trigonometry, 2e 62 

Conte Elementary Numerical Analysis: An Algorithmic Approach, 3e 120 

D 

DeFranza Introduction to Linear Algebra 111 

Don How to Solve Word Problems in Calculus 87, 93, 98 

Don Schaum’s Outline of Basic Business Mathematics, 2e 51 

Don Schaum’s Outline of Mathematica, 2e 92, 97 

Dowling Schaum’s Easy Outline of Introduction to Mathematical Economics 54 

Dowling Schaum’s Outline of Calculus for Business, Economics, and the Social Sciences 80 

Dowling Schaum’s Outline of Introduction to Mathematical Economics, 3e 52, 54 

Dowling Schaum’s Outline of Introduction to Mathematical Economics, Revised 3e 50 

Dowling Schaum’s Outline of Mathematical Methods for Business and Economics 50 

DuChateau Schaum’s Outline of Partial Differential Equations 107 

Dugopolski Algebra for College Students, 6e 37 

Dugopolski Elementary Algebra, 6e 16 

Dugopolski Elementary and Intermediate Algebra, 4e 19 

Dugopolski Intermediate Algeba, 7e 29 

Dumas Transition to Higher Mathematics: Structure and Proof 108, 110 

G 

Gibilisco Everyday Math Demystified 6 

Gibilisco Geometry Demystified 44 

Gibilisco Mastering Technical Mathematics, 3e 51 

Gibilisco Math Proofs Demystified 111 

Gibilisco Statistics Demystified 135 

Gibilisco Technical Math Demystified 52 

Gibilisco Trigonometry Demystified 64 

Gottfried Spreadsheet Tools for Engineers Using Excel, 3e 116 

150

H 

Author Index 

Hall Beginning and Intermediate Algebra: The Language and Symbolism of Mathematics, 3e 24 

Hoffmann Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition, 10e 79 

Hoffmann Calculus for Business, Economics, and the Social and Life Sciences, Brief Edition, 10e 79 

Huettenmueller Business Calculus Demystified 80 

Huettenmueller College Algebra Demystified 62 

Huettenmueller Pre-Calculus Demystified 74 

Hutchinson Elementary and Intermediate Algebra: Alternate Hardcover Edition, 3e 27 

Hutchinson Intermediate Algebra 35 

Hutchison Prealgebra, 2e 9 

I 

Immergut Arithmetic and Algebra Again, 2e 6, 10, 18 

J 

Jaisingh Schaum’s Outline of Abstract Algebra, 2e 127 

Jaisingh Statistics for the Utterly Confused, 2e 135 

K 

Kay Schaum’s Outline of Tensor Calculus 116, 117 

Kazmier Schaum’s Easy Outline of Business Statistics 134 

Krantz Differential Equations Demystified 103, 105 

Kruglak Schaum’s Outline of Basic Mathematics with Applications to Science and Technology, 2e 51 

Kutner Applied Linear Statistical Models, 5e 140 

L 

LaBelle Supersymmetry Demystified 51 

Ledder Differential Equations: A Modeling Approach 102 

Lindstrom Schaum’s Easy Outline of Statistics, 2e 132 

Lipschutz Schaum’s 2,000 Solved Problems in Discrete Mathematics 49 

Lipschutz Schaum’s 3,000 Solved Problems in Linear Algebra 113 

Lipschutz Schaum’s Easy Outlines: Linear Algebra 113 

Lipschutz Schaum’s Outline of Beginning Finite Mathematics 52, 53 

Lipschutz Schaum’s Outline of Beginning Linear Algebra 113 

Lipschutz Schaum’s Outline of Differential Geometry 121 

Lipschutz Schaum’s Outline of Discrete Mathematics, Revised 3e 49 

Lipschutz Schaum’s Outline of General Topology 127 

Lipschutz Schaum’s Outline of Introduction to Probability and Statistics 134 

Lipschutz Schaum’s Outline of Linear Algebra, 4e 113 

Lipschutz Schaum’s Outline of Probability, 2e 132 

Lipschutz Schaum’s Outline of Set Theory and Related Topics, 2e 135 

151

M 

Author Index 

Ma Five Steps to a 5 AP Calculus AB and BC, 3e 98 

McMahon Complex Variables Demystified 124 

McMahon Linear Algebra Demystified 114 

Mendelson Schaum’s 3,000 Solved Problems in Calculus 92 

Mendelson Schaum’s Outline of Beginning Calculus, 3e 73, 92 

Mendelson Schaum’s Outline of Boolean Algebra and Switching Circuits 49 

Mendenson Schaum’s Easy Outline of Calculus, 2e 91 

Messersmith Beginning Algebra 12 

Messersmith Beginning and Intermediate Algebra, 3e 21 

Messersmith Intermediate Algebra 31 

Miller Basic College Mathematics, 2e 4 

Miller Beginning Algebra, 3e 14 

Miller Beginning and Intermediate Algebra, 3e 25 

Miller Bob Miller’s Algebra for the Clueless, 2e 18 

Miller Bob Miller’s Calc for the Clueless: Calc I, 2e 87, 93 

Miller Bob Miller’s Calc for the Clueless: PreCalc, 3e 75 

Miller Intermediate Algebra, 2e 34 

Miller Intermediate Algebra, 3e 32 

Miller Introductory Algebra, 2e 15 

Miller Miller’s Geometry for the Clueless, 2e 43 

Miller Prealgebra 7 

Milton Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, 139 

4e 

Mood Introduction to the Theory of Statistics, 3e 136 

Moyer Schaum’s Easy Outline of College Algebra, 2e 62 

Moyer Schaum’s Outline of College Algebra, 3e 62 

Moyer Schaum’s Outline of Trigonometry, 4e 64 

N 

Navidi Principles of Statistics for Engineers and Scientists 139 

Navidi Statistics for Engineers and Scientists, 3e 138 

Nicholson Elementary Linear Algebra, 2e 112 

Nicholson Linear Algebra with Applications, 6e 112 

Nolt Schaum’s Easy Outline of Logic 126 

P 

Pallant SPSS Survival Manual, 4e 136 

Pevalin Stata Survival Guide (The) 137 

Polisky Solving Business Problems Using a Calculator Student Text, 6e 53 

Pritchard Mathcad: A Tool for Engineers and Scientists (B.E.S.T. Series), 2e 115 

152

R 

Author Index 

Ramana Higher Engineering Mathematics 116 

Rich Schaum’s Easy Outlines: Geometry, 2e 43 

Rich Schaum’s Outline of Elementary Algebra, 3e 17 

Rich Schaum’s Outline of Geometry, 4e 43 

Rich Schaum’s Outline of Review of Elementary Mathematics, 2e 5 

Rosen Discrete Mathematics and Its Applications, 7e 48 

Rudin Functional Analysis, 2e 124 

Rudin Principles of Mathematical Analysis, 3e 110, 118 

Rudin Real and Complex Analysis, 3e 109, 123, 125 

S 

Safier Schaum’s Outline of Precalculus, 2e 74 

Scheid Schaum’s Outline of Numerical Analysis, 2e 120 

Schiller Schaum’s Outline of Probability and Statistics, 3e 136 

Simmons Calculus with Analytic Geometry, 2e 84 

Simmons Differential Equations with Applications and Historical Notes, 2e 103 

Simmons Differential Equations: Theory, Technique, and Practice 101, 104 

Smith Calculus, 4e 81 

Smith Calculus, Single Variable: Late Transcendental Functions, 3e 88 

Smith Calculus: Concepts and Connections 83 

Smith Calculus: Early Transcendental Functions, 4e 82, 87, 93 

Smith Calculus: Multivariable: Early Transcendental Functions, 3e 96 

Smith Calculus: Multivariable: Late Transcendental Functions, 3e 94 

Smith Calculus: Single Variable: Early Transcendental Functions, 3e 90 

Sobecki Mathematics in Our World, 2e 44 

Spiegel Schaum’s Easy Outlines: Mathematical Handbook of Formulas and Tables 126 

Spiegel Schaum’s Outline of Advanced Mathematics for Engineers and Scientists 117 

Spiegel Schaum’s Outline of Calculus of Finite Differences and Difference Equations 119 

Spiegel Schaum’s Outline of College Algebra, 3e 39 

Spiegel Schaum’s Outline of Complex Variables, 2e 124 

Spiegel Schaum’s Outline of Fourier Analysis with Applications to Boundary Value Problems 107 

Spiegel Schaum’s Outline of Laplace Transforms 103, 105, 107 

Spiegel Schaum’s Outline of Mathematical Handbook of Formulas and Tables, 3e 39, 126 

Spiegel Schaum’s Outline of Probability and Statistics, 2e 134 

Spiegel Schaum’s Outline of Statistics, 4e 133, 141 

Steege Schaum’s Easy Outline Intermediate Algebra 37 

Steege Schaum’s Outline of Intermediate Algebra, 2e 36 

Stephens Advanced Statistics Demystified 141 

Stephens Engineering Statistics Demystified 140 

Stephens Schaum’s Outline of Beginning Statistics, 2e 133 

Stephens Schaum’s Outline of Business Statistics, 2e 133 

Stephens Schaum’s Outline of Mathematics for Nurses 52 

Stephens Schaum’s Outline of Statistics in Psychology 137 

153

T 

Author Index 

Thomas Schaum’s Outline of Mathematics for Liberal Arts Majors 45 

Trivieri Test Yourself: Elementary Algebra 19 

V 

Van Glabek Test Yourself: Intermediate Algebra 37 

W 

Wayne How to solve Math Word Problems on Standardized Tests 6, 10, 18 

Wayne How to solve Word Problems in Mathematics 7, 11, 19 

Wrede Schaum’s Outline of Advanced Calculus, 3e 86, 119 

Y 

Yang Multivariate Statistical Methods in Quality Management 140 

Z 

Zima Schaum’s Outline of Mathematics of Finance, 2e 54 

154

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