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MATHEMATICS & STATIS - Mcgraw-hill.com.sg

2010

MATHEMATICS & STATISTICS


McGRAW-HILL 2010 CATALOG

Welcome to McGraw-Hill’s 2010 Mathematics & Statistics Catalog. Inside

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CONTENTS

Developmental Mathematics

Algebra for College Students. . . . . . . . . . . . . . . . . . . . . . .32

Arithmetic/Basic Math .............................5

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

Beginning/Intermediate Algebra Combined ............16

Intermediate Algebra .............................25

PreAlgebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Mathematics Service Courses

Discrete Mathematics . ...........................40

Geometry ......................................35

Liberal Arts Mathematics ..........................36

Mathematics for Elementary Teachers ...............39

Professional References ..........................42

Technical Mathematics . ..........................42

Precalculus

College Algebra .................................47

College Algebra with Trigonometry . .................53

Precalculus . ...................................56

Trigonometry ...................................51

Calculus

Applied/Business Calculus . .......................65

Calculus and Analytic Geometry . ...................67

Multi-Variable Calculus . ..........................76

Professional References ..........................79

Single Variable Calculus . .........................72

Higher Mathematics

Advanced Engineering Mathematics .................92

Advanced Geometry .............................99

Combinatorics . .................................90

Complex Analysis . .............................100

Differential Equations . ...........................83

Differential Equations with Boundary Value Problems . . .85

Functional Analysis . ............................103

Graph Theory . .................................93

History of Mathematics ...........................95

Introductory Analysis .............................94

Linear Algebra ..................................88

Number Theory .................................98

Numerical Analysis ..............................96

Partial Differential Equations .......................86

Professional References .........................105

Real Analysis ..................................104

Transition to Higher Math/Foundations of Higher Math . . .87

Statistics and Probability

Advanced Statistics .............................118

Applied Statistics - Education, Psychology and Social

Science . ..................................114

Applied Statistics - Engineering ....................116

Statistics and Probability (Calculus) . ...............113

Statistics and Probabilitty (Non-Calculus) ............109

Indexes

Author Indexes . ...............................127

Title Indexes . .................................121


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NEW TITLES

DEVELOPMENT MATHEMATICS

2011 Author ISBN-13 Page

Basic College Mathematics, 4e Bello 9780077350079 5

Beginning and Intermediate Algebra, 3e Hall 9780077350048 17

Beginning Algebra, 3e Miller 9780077349936 11

Intermediate Algebra, 3e Miller 9780077349943 25

PreAlgebra Miller 9780077349950 8

DEVELOPMENT MATHEMATICS

2010 Author ISBN-13 Page

Hutchinson’s Basic Mathematical Skills with Geometry, 8e Baratto 9780077354749 5

Hutchinson’s Beginning Algebra, 8e Baratto 9780077354756 12

Hutchinson’s Elementary and Intermediate Algebra, 4e Baratto 9780077350123 16

PreAlgebra, Media Enhanced Edition, 3e Baratto 9780077299620 9

Beginning and Intermediate Algebra, 3e Miller 9780077350086 18

Intermediate Algebra, 2e Miller 9780077281113 27

MATHEMATICS SERVICE COURSES

2011 Author ISBN-13 Page

Mathematics in Our World, 2e Sobecki 9780077356651 36

MATHEMATICS SERVICE COURSES

2010 Author ISBN-13 Page

Mathematics for Elementary Teachers: A Conceptual Approach, 8e Bennett 9780077297930 39

Mathematics for Elementary Teachers: An Activity Approach, 8e Bennett 9780077297947 39


NEW TITLES

PRECALCULUS

2011 Author ISBN-13 Page

College Algebra, 9e Barnett 9780077350161 47

College Algebra with Trigonometry, 9e Barnett 9780077350109 53

PreCalculus, 7e Barnett 9780077349912 56

Trigonometry, 2e Coburn 9780077349974 51

PRECALCULUS

2010 Author ISBN-13 Page

Algebra & Trigonometry, 2e Coburn 9780077276515 54

College Algebra, 2e Coburn 9780077276492 48

College Algebra Essentials, 2e Coburn 9780077297909 49

PreCalculus, 2e Coburn 9780077276508 57

CALCULUS

2010 Author ISBN-13 Page

Applied Calculus for Business, Economics, and the Social and Life Sciences, Hoffmann 9780077297886 65

Expanded Edition

Calculus for Business, Economics, and the Social and Life Sciences, 10e Hoffmann 9780077292737 66


NEW TITLES

HIGHER MATHEMATICS

2011 Author ISBN-13 Page

Elementary Number Theory, 7e Burton 9780077349905 98

The History of Mathematics: An Introduction, 7e Burton 9780073383156 95

HIGHER MATHEMATICS

2010 Author ISBN-13 Page

Numerical Methods for Engineers, 6e Chapra 9780073401065 96

STATISTICS AND PROBABILITY

2011 Author ISBN-13 Page

Statistics for Engineers and Scientists, 3e Navidi 9780073376332 116

STATISTICS AND PROBABILITY

2010 Author ISBN-13 Page

Elementary Statistics: A Step by Step Approach, 7e Bluman 9780077302351 109

Biostatistics for the Health Sciences [An Asian Publication] Chinna 9789833850686 114

Principles of Statistics for Engineers and Scientists Navidi 9780077289317 116


NEW TITLES


DEVELOPMENTAL

MATHEMATICS

Algebra for College Students..............................................................................32

Arithmetic/Basic Math ...........................................................................................5

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

Beginning/Intermediate Algebra Combined ........................................................16

Intermediate Algebra ..........................................................................................25

PreAlgebra............................................................................................................8


NEW TITLES

DEVELOPMENT MATHEMATICS

2011 Author ISBN-13 Page

Basic College Mathematics, 4e Bello 9780077350079 5

Beginning and Intermediate Algebra, 3e Hall 9780077350048 17

Beginning Algebra, 3e Miller 9780077349936 11

Intermediate Algebra, 3e Miller 9780077349943 25

PreAlgebra Miller 9780077349950 8

DEVELOPMENT MATHEMATICS

2010 Author ISBN-13 Page

Hutchinson’s Basic Mathematical Skills with Geometry, 8e Baratto 9780077354749 5

Hutchinson’s Beginning Algebra, 8e Baratto 9780077354756 12

Hutchinson’s Elementary and Intermediate Algebra, 4e Baratto 9780077350123 16

PreAlgebra, Media Enhanced Edition, 3e Baratto 9780077299620 9

Beginning and Intermediate Algebra, 3e Miller 9780077350086 18

Intermediate Algebra, 2e Miller 9780077281113 27


DEVELOPMENTAL MATHEMATICS

Arithmetic/Basic Math

NEW


BASIC COLLEGE MATHEMATICS

Fourth Edition


2011 (January 2010) /

ISBN: 9780077350079


NEW


HUTCHINSON’S BASIC

MATHEMATICAL SKILLS WITH

GEOMETRY

Eighth Edition



2010 (October 2009) / Softcover

ISBN: 9780077354749


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.

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

8.4 Square Roots and the Pythagorean Theorem

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


1 Operations on Whole Numbers

1.1 The Decimal Place-Value System

1.2 Addition

1.3 Subtraction

1.4 Rounding, Estimation, and Order

1.5 Multiplication

1.6 Division


DEVELOPMENTAL MATHEMATICS

BASIC COLLEGE MATHEMATICS

Second Edition



2009 (October 2008) / Paper / 832 pages

ISBN: 9780077281137


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.


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

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

4.2 Addition and Subtraction of Decimals

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

5.3 Proportions

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

8.1 Lines and Angles

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

9.4 Mean, Median, and Mode

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

10.5 Order of Operations

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

BASIC COLLEGE MATHEMATICS

Third Edition


2009 (January 2008) / Softcover / 608 pages

ISBN: 9780077217884


Basic College Mathematics 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.


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


DEVELOPMENTAL MATHEMATICS

2.3 Multiplication and Division of Fractions and Mixed Numbers

2.4 Addition and Subtraction of Fractions

2.5 Addition and Subtraction of Mixed Numbers

2.6 Order of Operations and Grouping Symbols

2.7 Equations and Problem Solving

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

3.5 Equations and Problem Solving

4. RATIO, RATE, AND PROPORTION

4.1 Ratio and Proportion

4.2 Rates

4.3 Word Problems 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 Linear (Length) Measures

7.2 The Metric System

7.3 Converting Between American and Metric Units

7.4 Converting Units of Area

7.5 Capacity

7.6 Weight and Temperature

8. GEOMETRY

8.1 Finding Perimeters

8.2 Finding Areas

8.3 Volume of Solids

8.4 Angles and Triangles

8.5 Square Roots and Pythagoras’ 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

SCHAUM’S A-Z MATHEMATICS


2004 / 288 pages

ISBN: 9780071419369


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

Second Edition



1997 / 288 pages

ISBN: 9780070522794





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






Visit McGraw-Hill Education (Asia)

Website: www.mheducation.asia


DEVELOPMENTAL MATHEMATICS

NEW

PreAlgebra


PREALGEBRA



2011 (January 2010) / Softcover

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.


Chapter 1 Whole Numbers

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

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


DEVELOPMENTAL MATHEMATICS

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

NEW


PREALGEBRA

Media Enhanced Edition

Third Edition



2010 (January 2009)

ISBN: 9780077299620


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.


Integration of Videos: In the videos, qualified teachers work

through selected exercises from the text book, following the solution

methodology employed in the text. These are designated with marginal

icons for easy student reference. The videos can be viewed via the

text website for free, downloaded to their computers, or viewed on

their iPod/MP3 players.

ALEKS Integration: Students now have two modes of studying

Prealgebra using ALEKS. Students can use ALEKS in it’s current

model of taking an assessment and learning mathematics at their own

pace based on their strengths and weaknesses, or they can follow

along with their instructor and master these topics at the chapter level

where ALEKS will use artificial intelligence to determine mastery of

those particular topics.


CHAPTER 1 Whole Numbers

Pretest Chapter 1

1.1 Introduction to Whole Numbers and Place Value

1.2 Addition of Whole Numbers

1.3 Subtraction 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

Pretest Chapter 2

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

2.7 Evaluating Algebraic Expressions

2.8 Simplifying Algebraic Expressions

2.9 Introduction to Linear Equations

2.10 The Addition Property of Equality

Summary

Summary Exercises

Self-Test for Chapter 2

Cumulative Review for Chapters 1 to 2

CHAPTER 3 Fractions and Equations

Pretest Chapter 3

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

Summary Exercises

Self-Test for Chapter 3

Cumulative Review for Chapters 1 to 3

CHAPTER 4 Applications of Fractions and Equations

Pretest Chapter 4

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

Summary Exercises

Self-Test for Chapter 4

Cumulative Review for Chapters 1 to 4

CHAPTER 5 Decimals

Pretest Chapter 5

5.1 Introduction to Decimals, Place Value, and Rounding

5.2 Addition and Subtraction of Decimals

5.3 Multiplication of Decimals

5.4 Division of Decimals

5.5 Fractions and Decimals

5.6 Equations Containing Decimals

5.7 Square Roots and the Pythagorean Theorem

5.8 Applications

Summary

Summary Exercises

Self-Test for Chapter 5

Cumulative Review for Chapters 1 to 5

CHAPTER 6 Ratio, Rate, and Proportion

Pretest Chapter 6

6.1 Ratios

6.2 Rates

6.3 Proportions

6.4 Similar Triangles and Proportions

6.5 Linear Measurement and Conversion

Summary

Summary Exercises

Self-Test for Chapter 6

Cumulative Review for Chapters 1 to 6

CHAPTER 7 Percent

Pretest Chapter 7

7.1 Percents, Decimals, and Fractions


DEVELOPMENTAL MATHEMATICS

7.2 Solving Percent Problems Using Proportions

7.3 Solving Percent Applications Using Equations

7.4 Applications: Simple and Compound Interest

7.5 More Applications of Percent

Summary

Summary Exercises

Self-Test for Chapter 7

Cumulative Review for Chapters 1 to 7

CHAPTER 8 Geometry

Pretest Chapter 8

8.1 Lines and Angles

8.2 Perimeter and Circumference

8.3 Area and Volume

Summary

Summary Exercises

Self-Test for Chapter 8

Cumulative Review for Chapters 1 to 8

CHAPTER 9 Graphing and Introduction to Statistics

Pretest Chapter 9

9.1 Tables and Graphs of Data

9.2 The Rectangular Coordinate System

9.3 Linear Equations in Two Variables

9.4 Mean, Median, and Mode

Summary

Summary Exercises

Self-Test for Chapter 9

Cumulative Review for Chapters 1 to 9

CHAPTER 10 Polynomials

Pretest Chapter 10

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

Summary Exercises

Self-Test for Chapter 10

Practice Final Exam

PREALGEBRA

Second Edition



2007 (December 2005) / Softcover

ISBN: 9780073250335 (with MathZone)



CHAPTER 1 Whole Numbers

Pretest Chapter 1

1.1 Introduction to Whole Numbers, Place Value

1.2 Addition of Whole Numbers

1.3 Subtraction 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

1.8 Order of Operations

1.9 An Introduction to Equations

Summary

Summary and Review Exercises

Chapter Test

CHAPTER 2 Integers and Introduction to Algebra

Pretest Chapter 2

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

2.7 Evaluating Algebraic Expressions

2.8 Simplifying Algebraic Expressions

2.9 Introduction to Linear Equations

2.10 The Addition Property of Equality

Summary

Summary and Review Exercises

Chapter Test

Cumulative Test for Chapters 1 and 2

CHAPTER 3 Fractions and Equations

Pretest Chapter 3

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

Summary and Review Exercises

Chapter Test

Cumulative Test for Chapters 1 to 3

CHAPTER 4 Applications of Fractions and Equations

Pretest Chapter 4

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

4.6 Applications of Linear Equations in One Variable

Summary

Summary and Review Exercises

Chapter Test Cumulative Test for Chapters 1 to 4

CHAPTER 5 Decimals

Pretest Chapter 5

5.1 Introduction to Decimals, Place Value, and Rounding

5.2 Addition and Subtraction of Decimals

5.3 Multiplication of Decimals

5.4 Division of Decimals

5.5 Fractions and Decimals

5.6 Equations Containing Decimals

5.7 Square Roots and the Pythagorean Theorem

5.8 Applications

Summary

Summary and Review Exercises

Chapter Test Cumulative Test for Chapters 1 to 5

CHAPTER 6 Ratio, Rate, and Proportion

Pretest Chapter 6

6.1 Ratios

6.2 Rates

6.3 Proportions

6.4 Similar Triangles and Proportions

6.5 More Applications of Proportion

6.6 Linear Measurement and Conversion

Summary

Summary and Review Exercises

Chapter Test Cumulative Test for Chapters 1 to 6

CHAPTER 7 Percent

Pretest Chapter 7

7.1 Percents, Decimals, and Fractions

7.2 Solving Percent Problems Using Proportions

7.3 Solving Percent Applications Using Equations

7.4 Applications: Simple and Compound Interest

7.5 More Applications of Percent Summary

Summary and Review Exercises

Chapter Test Cumulative Test for Chapters 1 to 7

CHAPTER 8 Geometry

Pretest Chapter 8

8.1 Lines and Angles

8.2 Perimeter and Circumference

8.3 Area and Volume


DEVELOPMENTAL MATHEMATICS

Summary

Summary and Review Exercises

Chapter Test. Cumulative Test for Chapters 1 to 8

CHAPTER 9 Graphing and Introduction to Statistics

Pretest Chapter 9

9.1 Circle Graphs

9.2 Pictographs, Bar Graphs, and Line Graphs

9.3 The Rectangular Coordinate System

9.4 Linear Equations in Two Variables

9.5 Mean, Median, and Mode

Summary

Summary and Review Exercises

Chapter Test. Cumulative Test for Chapters 1 to 9

CHAPTER 10 Polynomials

Pretest Chapter 10

10.1 Introduction to Polynomials

10.2 Addition and Subtraction of Polynomials

10.3 Multiplying Polynomials

10.4 Introduction to Factoring Polynomials

Summary

Summary and Review Exercises

Chapter Test. Practice Final Exam Chapters 1 to 10

NEW

Beginning Algebra

2011 (January 2010) / Hardcover

ISBN: 9780077349936




BEGINNING ALGEBRA

Third Edition



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.


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

1.2 Order of Operations

1.3 Addition of Real Numbers

1.4 Subtraction of Real Numbers

1.5 Multiplication and Division 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

2.2 Solving Linear Equations

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

3.2 Linear Equations in Two Variables

3.3 Slope of a Line

3.4 Slope-Intercept Form of a Line

3.5 Point-Slope Formula

3.6 Applications of Linear Equations

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

4.5 Linear Inequalities 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

5.4 Scientific Notation

5.5 Addition and Subtraction of Polynomials

5.6 Multiplication of Polynomials

5.7 Division of Polynomials


DEVELOPMENTAL MATHEMATICS

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

7.1 Introduction to Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Least Common Denominator

7.4 Addition and Subtraction of Rational Expressions

7.5 Complex Fractions

7.6 Rational Equations

7.7 Applications of Rational Equations and Proportions

7.8 Variations

8 Radicals

8.1 Introducion to Roots and Radicals

8.2 Simplifying Radicals

8.3 Addition and Subtraction of Radicals

8.4 Multiplication of Radicals

8.5 Rationalization

8.6 Radical Equations

8.7 Rational Exponents

9 Functions, Complex Numbers, and Quadratic Equations

9.1 Introduction to Functions

9.2 Complex Numbers

9.3 The Square Root Property and Completing the Square

9.4 Quadratic Formula

9.5 Graphing Quadratic Functions

NEW


HUTCHINSON’S BEGINNING

ALGEBRA

Eighth Edition



2010 (November 2009) / Softcover

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.

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

2.5 Applications of Linear Equations

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

3.4 Multiplying 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

4.6 Solving Quadratic Equations by Factoring

5 Rational Expressions

5.1 Simplifying Rational Expressions

5.2 Multiplying and Dividing Rational Expressions

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

6.2 The Rectangular Coordinate System

6.3 Graphing Linear Equations

6.4 The Slope of a Line

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

8.4 Systems of Linear Inequalities

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


1 The Language of Algebra

1.1 Properties of Real Numbers

1.2 Adding and Subtracting Real Numbers

1.3 Multiplying and Dividing Real Numbers

1.4 From Arithmetic to Algebra

1.5 Evaluating Algebraic Expressions

1.6 Adding and Subtracting Terms

1.7 Multiplying and Dividing Terms

2 Equations and Inequalities


DEVELOPMENTAL MATHEMATICS

INTRODUCTORY ALGEBRA

Third Edition


2009 (January 2008) / 800 pages

ISBN: 9780077224783


Introductory Algebra prepares students for Intermediate Algebra by

covering fundamental algebra concepts and key concepts needed


a refreshing book that appeals to every learning style 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

algebra in the real world.


Introductory Algebra

Chapter R: Prealgebra Review

R.1 Fractions: Building and Reducing

R.2 Operations with Fractions and Mixed Numbers

R.3 Decimals and Percents

Chapter 1: Real Numbers and Their Properties

1.1 Introduction to Algebra

1.2 The Real Numbers

1.3 Adding and Subtracting Real Numbers

1.4 Multiplying and Dividing Real Numbers

1.5 Order of Operations

1.6 Properties of the Real Numbers

1.7 Simplifying Expressions

Chapter 2: Equations, Problem Solving, and Inequalities

2.1 The Addition 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

Chapter 3: Graphs of Linear Equations, Inequalities, and Applications

3.1 Line, 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 Slopes

3.6 Applications of Equations of Lines

3.7 Graphing Inequalities in Two Variables

Chapter 4: Exponents and Polynomials

4.1 The Product, Quotient, and Power Rules for Exponents

4.2 Integer Exponents

4.3 Application of Exponents: Scientific Notation

4.4 Polynomials: An Introduction

4.5 Addition and Subtraction of Polynomials

4.6 Multiplication of Polynomials

4.7 Special Products of Polynomials

4.8 Division of Polynomials

Chapter 5: Factoring

5.1 Common Factors and Grouping

5.2 Factoring x^2+bx+c

5.3 Factoring ax^2+bx+c, a¿0

5.4 Factoring Squares of Binomials

5.5 A General Factoring Strategy

5.6 Solving Quadratic Equations by Factoring

5.7 Applications of Quadratics

Chapter 6: Rational Expressions

6.1 Building and Reducing Rational Expressions

6.2 Multiplication and Division of Rational Expressions

6.3 Addition and Subtraction of Rational Expressions

6.4 Complex Fractions

6.5 Solving Equations Containing Rational Expressions

6.6 Ratio, Proportion, and Applications

6.7 Direct and Inverse Variation

Chapter 7: Solving Systems of Linear Equations and Inequalities

7.1 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

Chapter 8: Roots and Radicals

8.1 Finding Roots

8.2 Multiplication and Division of Radicals

8.3 Addition and Subtraction of Radicals

8.4 Simplifying Radicals

8.5 Applications

Chapter 9: Quadratic Equations

9.1 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

INTRODUCTORY ALGEBRA

Alternate Edition (Hardback)

Second Edition



2009 (November 2008) / 832 pages

ISBN: 9780077281120

ISBN: 9780077303877 [Alternate Edition 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



Chapter 1: The Set of Real Numbers

1.1 Sets of Numbers and the Real Number Line

1.2 Order of Operations

1.3 Addition of Real Numbers

1.4 Subtraction of Real Numbers--Problem Recognition Exercises—

Addition and Subtraction of Signed Numbers

1.5 Multiplication and Division of Real Numbers

1.6 Properties of Real Numbers and Simplifying Expressions

Chapter 2: Linear Equations and Inequalities

2.1 Addition, Subtraction, Multiplication, and Division Properties of

Equality

2.2 Solving Linear Equations

2.3 Linear Equations: Clearing Fractions and Decimals--Problem

Recognition Exercises—Equations and Expressions

2.4 Applications of Linear Equations: Introduction to Problem Solving

2.5 Applications Involving Percents

2.6 Formulas and Applications of Geometry

2.7 Mixture Applications and Uniform Motion

2.8 Linear Inequalities

Chapter 3: Graphing Linear Equations in Two Variables

3.1 Rectangular Coordinate System

3.2 Linear Equations in Two Variables

3.3 Slope of a Line

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

Linear Equations in Two Variables

3.5 Point-Slope Formula

3.6 Applications of Linear Equations


DEVELOPMENTAL MATHEMATICS

3.7 Introduction to Functions

Chapter 4: Systems of Linear Equations 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--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

5.1 Exponents: Multiplying and Dividing Common Bases

5.2 More Properties of Exponents

5.3 Definitions of and

5.4 Scientific Notation--Problem Recognition Exercises—Properties

of Exponents

5.5 Addition and Subtraction of Polynomials

5.6 Multiplication of Polynomials

5.7 Division of Polynomials--Problem Recognition Exercises—Operations

on Polynomials

Chapter 6: Factoring Polynomials

6.1 Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the Form

6.3 Factoring Trinomials: Trial-and-Error Method

6.4 Factoring Trinomials: AC-Method

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

6.8 Applications of Quadratic Equations

Chapter 7: Rational Expressions

7.1 Introduction to Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Least Common Denominator

7.4 Addition and Subtraction of Rational Expressions--Problem Recognition

Exercises—Operations on Rational Expressions

7.5 Complex Fractions

7.6 Rational Equations--Problem Recognition Exercises—Comparing

Rational Equations and Rational Expressions

7.7 Applications of Rational Equations and Proportions

7.8 Variation

Chapter 8: Radicals

8.1 Introduction to Roots and Radicals

8.2 Simplifying Radicals

8.3 Addition and Subtraction of Radicals

8.4 Multiplication of Radicals

8.5 Division of Radicals and Rationalization--Problem Recognition

Exercises—Operations on Radicals

8.6 Radical Equations

8.7 Rational Exponents

Chapter 9: More Quadratic Equations

9.1 The Square Root Property

9.2 Completing the Square

9.3 Quadratic Formula--Problem Recognition Exercises—Solving

Quadratic Equations

9.4 Graphing Quadratic Functions

ELEMENTARY ALGEBRA

Sixth Edition


2009 (January 2008)

ISBN: 9780077224790


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

useful supplements, including McGraw-Hill’s online homework

management system, MathZone.


TO THE STUDENT

PREFACE

1 Real Numbers and Their Properties

1.1 The Real Numbers

1.2 Fractions

1.3 Addition and Subtraction of Real Numbers

1.4 Multiplication and Division of Real Numbers

1.5 Exponential Expressions and the Order of Operations

1.6 Algebraic Expressions

1.7 Properties of the Real Numbers

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

Chapter 2 Wrap-Up







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

3.4 The Point-Slope Form


DEVELOPMENTAL MATHEMATICS

3.5 Variations

Chapter 3 Wrap-Up







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

Chapter 4 Wrap-Up







5 Exponents and Polynomials

5.1 The Rules of Exponents

5.2 Negative Exponents and Scientific Notation

5.3 Addition and Subtraction of Polynomials

5.4 Multiplication of Polynomials

5.5 Multiplication of Binomials

5.6 Special Products

5.7 Division of Polynomials

Chapter 5 Wrap-Up







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

6.6 Solving Quadratic Equations by Factoring

Chapter 6 Wrap-Up







7 Rational Expressions

7.1 Reducing Rational Expressions

7.2 Multiplication and Division

7.3 Finding the Least Common Denominator

7.4 Addition and Subtraction

7.5 Complex Fractions

7.6 Solving Equations with Rational Expressions

7.7 Applications of Ratios and Proportions

7.8 Applications of Rational Expressions

Chapter 7 Wrap-Up







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

Chapter 8 Wrap-Up







9 Quadratic Equations, Parabolas, and Functions

9.1 The Square Root Property and Factoring

9.2 Completing the Square

9.3 The Quadratic Formula

9.4 Applications of Quadratic Equations

9.5 Complex Numbers

9.6 Graphing Parabolas

9.7 Introduction to Functions

9.8 Combining Functions

Chapter 9 Wrap-Up







Appendix A: Geometry Review Exercises

Appendix B: Sets

Appendix C: Final Exam Review Answers to Selected Exercises Index

SCHAUM’S OUTLINE OF ELEMENTARY

ALGEBRA

Third Edition



2009 (May 2009) / 400 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


DEVELOPMENTAL MATHEMATICS

Beginning/Intermediate

Algebra Combined

NEW


HUTCHINSON’S ELEMENTARY

AND INTERMEDIATE

ALGEBRA

Fourth Edition



2011 (January 2010) / Hardcover

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.


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.


0 Prealgebra Review

0.1 A Review of Fractions

0.2 Real Numbers

0.3 Adding and Subtracting Real Numbers

0.4 Multiplying and Dividing Real Numbers

0.5 Exponents and Order of Operation

1 From Arithmetic to Algebra

1.1 Transition to Algebra

1.2 Evaluating Algebraic Expressions

1.3 Adding and Subtracting Algebraic Expressions

1.4 Sets

2 Functions and Graphs

2.1 Solving Equations by Adding and Subtracting

2.2 Solving Equations by Multiplying and Dividing

2.3 Combining the Rules to Solve Equations

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

3.1 Solutions of Equations in Two Variables

3.2 The Cartesian Coordinate System

3.3 The Graph of a Linear Equation

3.4 The Slope of a Line

3.5 Forms of Linear Equations

3.6 Graphing Linear Inequalities in Two Variables

4 Systems of Linear Equations

4.1 Positive Integer Exponents

4.2 Zero and Negative Exponents and Scientific Notation

4.3 Introduction to Polynomials


DEVELOPMENTAL MATHEMATICS

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials and Special Products

4.6 Division of Polynomials

5 Exponents and Polynomials

5.1 An Introduction to Factoring

5.2 Factoring Special Polynomials

5.3* Factoring Trinomials: Trial and Error

5.4 Factoring Trinomials: The ac method

5.5 Strategies in Factoring

5.6 Solving Quadratic Equations by Factoring

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 Factoring Polynomials

6.1 Relations and Functions

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

7.1 Simplifying Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions

7.4 Complex Fractions

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

8.3 Systems of Linear Equations in Three Variables

8.4 Systems of Linear Inequalities in Two Variables

8.5 Matrices (Optional)

9 Rational Expressions

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 Exponential and Logarithmic Functions

10.1 Roots and Radicals

10.2 Simplifying Radical Expressions

10.3 Operations on Radical Expressions

10.4 Solving Radical Equations

10.5 Rational Exponents

10.6 Complex Numbers

11 Quadratic Functions

11.1 Solving Quadratic Equations by Completing the Square

11.2 The Quadratic Formula

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 Exponential and Logarithmic Functions

13.1 Inverse Relations and Functions

13.2 Exponential Functions

13.3 Logarithmic Functions

13.4 Properties of Logarithms

13.5 Logarithmic and Exponential Equations

Appendix A

Appendix A.1 Determinants and Cramer’s Rule

NEW


BEGINNING AND INTERMEDIATE ALGEBRA

The Language and Symbolism of

Mathematics

Third Edition


2011 (January 2010)

ISBN: 9780077350048



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.


1 Operations with Real Numbers and a Review of Geome

1.1 Preparing for an Algebra Class

1.2 The Real Number Line

1.3 Addition of Real Numbers

1.4 Subtraction of Real Numbers

1.5 Multiplication of Real Numbers and Natural Number Exponents

1.6 Division of Real Numbers

1.7 Order of Operations

2 Linear Equations and Patterns

2.1 The Rectangular Coordinate System and Arithmetic Sequences

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


DEVELOPMENTAL MATHEMATICS

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

5.3 Negative Exponents and Scientific Notation

5.4 Adding and Subtracting Polynomials

5.5 Multiplying Polynomials

5.6 Special Products of Binomials

5.7 Dividing Polynomials

Diagonostic Review of Beginning Algebra

6 Factoring Polynomials

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

9.2 Multiplying and Dividing Rational Expressions

9.3 Adding and Subtracting 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

Cumulative Review of Chapters 1-8

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 Exponential and Logarithmic Functions

11.1 Geometric Sequences Graphs of Exponential Functions

11.2 Inverse Functions

11.3 Logarithmic Functions

11.4 Evaluating Logarithms

11.5 Properties of Logarithms

11.6 Solving Exponential and Logarithmic Equations

11.7 Exponential Curve Fitting and Other Applications of Exponential

and Logarithmic Equations

Cumulative Review of Chapters 1-10

12 A Preview of College Algebra

12.1 Solving Systems of Linear Equations by Using Augmented

Matrices

12.2 Systems of Linear Equations in Three Variables

12.3 Horizontal and Vertical Translations of the Graphs of Functions

12.4 Stretching, Shrinking and Reflecting Graphs of Functions

12.5 Algebra of Functions

12.6 Sequences, Series and Summation Notation

12.7 Conic Sections

NEW


BEGINNING AND

INTERMEDIATE ALGEBRA

Third Edition




2011 (January 2010)

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.


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.


DEVELOPMENTAL MATHEMATICS

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.”

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.


Chapter R: Reference

R.1 Study Tips

R.2 Fractions

R.3 Introduction to Geometry

Chapter 1: The Set of Real Numbers

1.1 Sets of Numbers and the Real Number Line

1.2 Order of Operations

1.3 Addition of Real Numbers

1.4 Subtraction of Real Numbers

Problem Recognition Exercises – Addition and Subtraction of Signed

Numbers

1.5 Multiplication and Division of Real Numbers

1.6 Properties of Real Numbers and Simplifying Expressions

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Test

Chapter 2: Linear Equations and Inequalities

2.1 Addition, Subtraction, Multiplication, and Division Properties

of Equality

2.2 Solving Linear Equations

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

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Test

Cumulative Review Exercises Chapters 1 – 2

Chapter 3: Graphing Linear Equations in Two Variables

3.1 Rectangular Coordinate System

3.2 Linear Equations in Two Variables

3.3 Slope of a Line

3.4 Slope-Intercept Form of a Line

3.5 Point-Slope Formula

3.6 Applications of Linear Equations

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Test

Cumulative Review Exercises Chapters 1 – 3

Chapter 4: Systems of Linear Equations 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

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Test

Cumulative Review Exercises Chapters 1 – 4

Chapter 5: Polynomials and Properties of Exponents

5.1 Exponents: Multiplying and Dividing Common Bases

5.2 More Properties of Exponents

5.3 Definitions of b0 and b-n

5.4 Scientific Notation Problem Recognition Exercises – Properties

of Exponents

5.5 Addition and Subtraction of Polynomials

5.6 Multiplication of Polynomials

5.7 Division of Polynomials

Problem Recognition Exercises – Operations on Polynomial

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Test

Cumulative Review Exercises, Chapters 1-5

Chapter 6: Factoring Polynomials

6.1 Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the form x2 + 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 by Using the Zero Product Rule

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Test

Cumulative Review Exercises Chapters 1 – 6

Chapter 7: Rational Expressions

7.1 Introduction to Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Least Common Denominator

7.4 Addition and Subtraction of Rational Expressions

Problem Recognition Exercises - Operations on Rational Expressions

7.5 Complex Fractions

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 7 Summary

Chapter 7 Review Exercises

Chapter 7 Test

Cumulative Review Exercises Chapters 1 – 7

Chapter 8: Introduction to Relations and Functions

8.1 Introduction to Relations

8.2 Introduction to Functions

8.3 Graphs of Functions

8.4 Variation


DEVELOPMENTAL MATHEMATICS

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Test

Cumulative Review Exercises, Chapters 1 – 8

Chapter 9: Systems of Linear Equations in Three Variables

9.1 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 9 Summary

Chapter 9 Review Exercises

Chapter 9 Test

Cumulative Review Exercises, Chapters 1 – 9

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

10.5 Linear Inequalities in Two Variables

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Test

Cumulative Review Exercises, Chapters 1 – 10

Chapter 11: Radicals and Complex Numbers

11.1 Definition of an nth-Root

11.2 Rational Exponents

11.3 Simplifying Radical Expressions

11.4 Addition and Subtraction of Radicals

11.5 Multiplication of Radicals

11.6 Rationalization

Problem Recognition Exercises – Operations on Radicals

11.7 Radical Equations

11.8 Complex Numbers

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Test

Cumulative Review Exercises, Chapters 1 – 11

Chapter 12: Quadratic Equations and Functions

12.1 Square Root Property and Completing the Square

12.2 Quadratic Formula

12.3 Equations in Quadratic Form

12.4 Graphs of Quadratic Functions

12.5 Vertex of a Parabola and Applications

Chapter 12 Summary

Chapter 12 Review Exercises

Chapter 12 Test

Cumulative Review Exercises, Chapters 1 – 12

Chapter 13: Exponential and Logarithmic Functions

13.1 Algebra and Composition of Functions

13.2 Inverse Functions

13.3 Exponential Functions

13.4 Logarithmic Functions

13.5 Properties of Logarithms

13.6 The Irrational Number, e

Problem Recognition Exercises - Logarithmic and Exponential Forms

13.7 Logarithmic and Exponential Equations

Chapter 13 Summary

Chapter 13 Review Exercises

Chapter 13 Test

Cumulative Review Exercises, Chapters 1 – 13

Chapter 14: Conic Sections and Nonlinear Systems

14.1 Distance Formulas and Circles

14.2 More on the Parabola

14.3 The Ellipse and Hyperbola

14.4 Nonlinear Systems of Equations in Two Variables

14.5 Nonlinear Inequalities and Systems of Inequalities

Chapter 14 Summary

Chapter 14 Review Exercises

Chapter 14 Test

Cumulative Review Exercises, Chapters 1 – 14

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

International Edition

ELEMENTARY AND INTERMEDIATE

ALGEBRA

Third Edition


2009 (January 2008)

ISBN: 9780077224820

ISBN: 9780071284028 [IE]


Elementary & 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


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.


TO THE STUDENT

PREFACE

1 Real Numbers and Their Properties

1.1 The Real Numbers

1.2 Fractions

1.3 Addition and Subtraction of Real Numbers

1.4 Multiplication and Division of Real Numbers

1.5 Exponential Expressions and the Order of Operations

1.6 Algebraic Expressions

1.7 Properties of the Real Numbers

1.8 Using the Properties to Simplify Expressions

Chapter 1 Wrap-Up


DEVELOPMENTAL MATHEMATICS


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

Chapter 2 Wrap-Up







3 Linear Equations and Inequalities in Two Variables

3.1 Graphing Lines in the Coordinate Plane

3.2 Slope

3.3 Equations of Lines in Slope-Intercept Form

3.4 The Point-Slope Form

3.5 Variations

3.6 Graphing Linear Inequalities in Two Variables

Chapter 3 Wrap-Up







4 Exponents and Polynomials

4.1 The Rules of Exponents

4.2 Negative Exponents and Scientific Notation

4.3 Addition and Subtraction of Polynomials

4.4 Multiplication of Polynomials

4.5 Multiplication of Binomials

4.6 Special Products

4.7 Division of Polynomials

Chapter 4 Wrap-Up







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 The Factoring Strategy

5.6 Solving Quadratic Equations by Factoring

Chapter 5 Wrap-Up







6 Rational Expressions

6.1 Reducing Rational Expressions

6.2 Multiplication and Division

6.3 Finding the Least Common Denominator

6.4 Addition and Subtraction

6.5 Complex Fractions

6.6 Solving Equations Involving Rational Expressions

6.7 Applications of Ratios and Proportions

6.8 Applications of Rational Expressions

Chapter 6 Wrap-Up







7 Systems of Linear Equations

7.1 Solving Systems by Graphing and Substitution

7.2 The Addition Method

7.3 Systems of Linear Equations in Three Variables

Chapter 7 Wrap-Up







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

Chapter 8 Wrap-Up







9 Radicals and Rational Exponents

9.1 Radicals

9.2 Rational Exponents

9.3 Adding, Subtracting, and Multiplying Radicals

9.4 Quotients, Powers, and Rationalizing Denominators

9.5 Solving Equations with Radicals and Exponents

9.6 Complex Numbers

Chapter 9 Wrap-Up







10 Quadratic Equations and Inequalities

10.1 Factoring and Completing the Square

10.2 The Quadratic Formula

10.3 More on Quadratic Equations

10.4 Graphing Parabolas

10.5 Quadratic and Rational Inequalities

Chapter 10 Wrap-Up







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

11.6 Combining Functions

11.7 Inverse Functions

Chapter 11 Wrap-Up


DEVELOPMENTAL MATHEMATICS

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

Chapter 12 Wrap-Up







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

Chapter 13 Wrap-Up







14 Sequences and Series

14.1 Sequences

14.2 Series

14.3 Arithmetic Sequences and Series

14.4 Geometric Sequences and Series

14.5 Binomial Expansions

Chapter 14 Wrap-Up







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








Visit McGraw-Hill Education

Website: www.mheducation.asia

BEGINNING AND INTERMEDIATE ALGEBRA

Second Edition


2009 (February 2008)

ISBN: 9780077224837


Beginning and Intermediate Algebra, 2e, by Messersmith is the


The author presents the content in bite-size pieces, focusing not only

on how to solve 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


core 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



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.

Messersmith – mapping the journey to mathematical success!


Chapter 1: The Real Number System and Geometry

Section 1.1 Review of Fractions

Section 1.2 Exponents and Order of Operations

Section 1.3 Geometry Review

Section 1.4 Sets of Numbers and Absolute Value

Section 1.5 Addition and Subtraction of Real Numbers

Section 1.6 Multiplication and Division of Real Numbers

Section 1.7 Algebraic Expressions and Properties of Real Numbers

Chapter 2: Variables and Exponents

Section 2.1 Simplifying Expressions

Section 2.2a The Product Rule and Power Rules for Exponents

Section 2.2b Combining the Rules

Section 2.3a Integer Exponents with Real-Number Bases

Section 2.3b Integer Exponents With Variable Bases

Section 2.4 The Quotient Rule

Mid-Chapter Summary

Section 2.5 Scientific Notation

Chapter 3: Linear Equations and Inequalities

Section 3.1 Solving Linear Equations Part I

Section 3.2 Solving Linear Equations Part II

Section 3.3 Applications of Linear Equations to General Problems,

Consecutive Integers, and Fixed and Variable Cost

Section 3.4 Applications of Linear Equations to Percent Increase/

Decrease and Investment Problems

Section 3.5 Geometry Applications and Solving Formulas for a

Specific Variable

Section 3.6 Applications of Linear Equations to Proportions, d = rt,

and Mixture Problems

Section 3.7 Solving Linear Inequalities in One Variable

Section 3.8 Solving Compound Inequalities

Chapter 4: Linear Equations in Two Variables

Section 4.1 Introduction to Linear Equations in Two Variables

Section 4.2 Graphing by Plotting Points and Finding Intercepts

Section 4.3 The Slope of a Line

Section 4.4 The Slope-Intercept Form of a Line

Section 4.5 Writing an Equation of a Line

Section 4.6 Parallel and Perpendicular Lines

Section 4.7 Introduction to Functions


DEVELOPMENTAL MATHEMATICS

Section 4.8 Function Notation and Linear Functions

Chapter 5: Solving Systems of Linear Equations

Section 5.1 Solving Systems by Graphing

Section 5.2 Solving Systems by Substitution

Section 5.3 Solving Systems by the Elimination Method

Mid-Chapter Summary

Section 5.4 Applications of Systems of Two Equations

Section 5.5 Systems of Linear Equations in Three Variables

Chapter 6: Polynomials

Section 6.1 Review of Rules of Exponents

Section 6.2 Addition and Subtraction of Polynomials

Section 6.3 Multiplication of Polynomials

Section 6.4 Division of Polynomials

Chapter 7: Factoring Polynomials

Section 7.1 The Greatest Common Factor and Factoring by Grouping

Section 7.2 Factoring Trinomials of the Form x^2 + bx + c

Section 7.3 Factoring Polynomials of the Form ax^2 + bx + c (a not

equal to 1)

Section 7.4 Factoring Binomials and Perfect Square Trinomials

Mid-Chapter Summary

Section 7.5 Solving Quadratic Equations by Factoring

Section 7.6 Applications of Quadratic Equations

Chapter 8: Rational Expressions

Section 8.1 Simplifying Rational Expressions

Section 8.2 Multiplying and Dividing Rational Expressions

Section 8.3 Finding the Least Common Denominator

Section 8.4 Adding and Subtracting Rational Expressions

Mid-Chapter Summary

Section 8.5 Simplifying Complex Fractions

Section 8.6 Solving Rational Equations

Section 8.7 Applications

Chapter 9: Absolute Value Equations and Inequalities

Section 9.1 Solving Absolute Value Equations

Section 9.2 Solving Absolute Value Inequalities

Section 9.3 Linear Inequalities in Two Variables

Section 9.4 Solving Systems of Equations Using Matrices

Chapter 10: Radicals and Rational Exponents

Section 10.1 Finding Roots

Section 10.2 Rational Exponents

Section 10.3 Simplifying Expressions Containing Square Roots

Section 10.4 Simplifying Expressions Containing Higher Roots

Section 10.5 Adding and Subtracting Radicals

Section 10.6 Combining Multiplication, Addition, and Subtraction of

Radicals

Section 10.7 Dividing Radicals

Section 10.8 Solving Radical Equations

Chapter 11: Quadratic Equations

Section 11.1 Review of Solving Equations by Factoring

Section 11.2 Solving Quadratic Equations Using the Square Root

Property

Section 11.3 Complex Numbers

Section 11.4 Solving Quadratic Equations by Completing the Square

Section 11.5 Solving Quadratic Equations Using the Quadratic

Formula

Mid-Chapter Summary

Section 11.6 Equations in Quadratic Form

Section 11.7 Formulas and Applications

Chapter 12: Functions and their Graphs

Section 12.1 Relations and Functions

Section 12.2 Graphs of Functions and Transformations

Section 12.3 Quadratic Functions and their Graphs

Section 12.4 Applications of Quadratic Functions and Graphing Other

Parabolas

Section 12.5 The Algebra of Functions

Section 12.6 Variation

Chapter 13: Inverse, Exponential, and Logarithmic Functions

Section 13.1 Inverse Functions

Section 13.2 Exponential Functions

Section 13.3 Logarithmic Functions

Section 13.4 Properties of Logarithms

Section 13.5 Common and Natural Logarithms and Change of Base

Section 13.6 Solving Exponential and Logarithmic Equations

Chapter 14: Conic Sections, Nonlinear Inequalities, and Nonlinear

Systems

Section 14.1 The Circle

Section 14.2 The Ellipse and the Hyperbola

Mid-Chapter Summary

Section 14.3 Nonlinear Systems of Equations

Section 14.4 Quadratic and Rational Inequalities

Chapter 15: Sequences and Series **Available online**

Section 15.1 Sequences and Series

Section 15.2 Arithmetic Sequences and Series

Section 15.3 Geometric Sequences and Series

Section 15.4 The Binomial Theorem

Appendix: Beginning Algebra Review

International Edition

ELEMENTARY AND INTERMEDIATE

ALGEBRA

3rd Edition



2008 (February 2007) / 1152 pages

ISBN: 9780073309613 (with MathZone)

ISBN: 9780071101936 [IE]


Elementary & Intermediate Algebra, 3/e by Baratto/Bergman is part

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

Mathematics. The third 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.


0 Prealgebra Review

0.1 A Review of Fractions

0.2 Real Numbers

0.3 Adding and Subtracting Real Numbers

0.4 Multiplying and Dividing Real Numbers

0.5 Exponents and Order of Operation

1 From Arithmetic to Algebra

1.1 Transition to Algebra

1.2 Evaluating Algebraic Expressions

1.3 Adding and Subtracting Algebraic Expressions

1.4 Sets

2 Equations and Inequalities

2.1 Solving Equations by Adding and Subtracting

2.2 Solving Equations by Multiplying and Dividing

2.3 Combining the Rules to Solve Equations

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)


DEVELOPMENTAL MATHEMATICS

2.8 Solving Absolute Value Inequalities (Optional)

3 Graphs and Linear Equations

3.1 Solutions of Equations in Two Variables

3.2 The Cartesian Coordinate System

3.3 The Graph of a Linear Equation

3.4 The Slope of a Line

3.5 Forms of Linear Equations

3.6 Graphing Linear Inequalities in Two Variables

4 Exponents and Polynomials

4.1 Positive Integer Exponents

4.2 Zero and Negative Exponents and Scientific Notation

4.3 Introduction to Polynomials

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials and Special Products

4.6 Division of Polynomials

5 Factoring Polynomials

5.1 An Introduction to Factoring

5.2 Factoring Special Polynomials

5.3* Factoring Trinomials: Trial and Error

5.4 Factoring Trinomials: The ac method

5.5 Strategies in Factoring

5.6 Solving Quadratic Equations by Factoring

5.7 Problem Solving with Factoring

6 A Beginning Look at Functions

6.1 Relations and Functions

6.2 Tables and Graphs

6.3 Algebra of Functions

6.4 Composition of Functions

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 Rational Expressions

7.1 Simplifying Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions

7.4 Complex Fractions

7.5 Solving Rational Expressions

7.6 Solving Rational Inequalities

8 Systems of Linear Equations and Inequalities

8.1 Solving Systems of Linear Equations by Graphing

8.2 Systems of Equations in Two Variables with Applications

8.3 Systems of Linear Equations in Three Variables

8.4 Systems of Linear Inequalities in Two Variables

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

10.1 Roots and Radicals

10.2 Simplifying Radical Expressions

10.3 Operations on Radical Expressions

10.4 Solving Radical Equations

10.5 Rational Exponents 10.6 Complex Numbers

11 Quadratic Functions

11.1 Solving Quadratic Equations by Completing the Square

11.2 The Quadratic Formula

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 Exponential and Logarithmic Functions

13.1 Inverse Relations and Functions

13.2 Exponential Functions

13.3 Logarithmic Functions

13.4 Properties of Logarithms

13.5 Logarithmic and Exponential Equations / Appendix A / Appendix

A.1 Determinants and Cramer’s Rule

ELEMENTARY AND INTERMEDIATE

ALGEBRA

Alternate Hardcover Edition

Third Edition



2008 (February 2007)

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.


0 Prealgebra Review

0.1 A Review of Fractions

0.2 Real Numbers

0.3 Adding and Subtracting Real Numbers

0.4 Multiplying and Dividing Real Numbers

0.5 Exponents and Order of Operation

1 From Arithmetic to Algebra

1.1 Transition to Algebra

1.2 Evaluating Algebraic Expressions

1.3 Adding and Subtracting Algebraic Expressions

1.4 Sets

2 Equations and Inequalities

2.1 Solving Equations by Adding and Subtracting

2.2 Solving Equations by Multiplying and Dividing

2.3 Combining the Rules to Solve Equations

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 Graphs and Linear Equations

3.1 Solutions of Equations in Two Variables

3.2 The Cartesian Coordinate System

3.3 The Graph of a Linear Equation

3.4 The Slope of a Line

3.5 Forms of Linear Equations

3.6 Graphing Linear Inequalities in Two Variables


DEVELOPMENTAL MATHEMATICS

4 Exponents and Polynomials

4.1 Positive Integer Exponents

4.2 Zero and Negative Exponents and Scientific Notation

4.3 Introduction to Polynomials

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials and Special Products

4.6 Division of Polynomials

5 Factoring Polynomials

5.1 An Introduction to Factoring

5.2 Factoring Special Polynomials

5.3* Factoring Trinomials: Trial and Error

5.4 Factoring Trinomials: The ac method

5.5 Strategies in Factoring

5.6 Solving Quadratic Equations by Factoring

5.7 Problem Solving with Factoring

6 A Beginning Look at Functions

6.1 Relations and Functions

6.2 Tables and Graphs

6.3 Algebra of Functions

6.4 Composition of Functions

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 Rational Expressions

7.1 Simplifying Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions

7.4 Complex Fractions

7.5 Solving Rational Expressions

7.6 Solving Rational Inequalities

8 Systems of Linear Equations and Inequalities

8.1 Solving Systems of Linear Equations by Graphing

8.2 Systems of Equations in Two Variables with Applications

8.3 Systems of Linear Equations in Three Variables

8.4 Systems of Linear Inequalities in Two Variables

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

10.1 Roots and Radicals

10.2 Simplifying Radical Expressions

10.3 Operations on Radical Expressions

10.4 Solving Radical Equations

10.5 Rational Exponents

10.6 Complex Numbers

11 Quadratic Functions

11.1 Solving Quadratic Equations by Completing the Square

11.2 The Quadratic Formula

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 Exponential and Logarithmic Functions

13.1 Inverse Relations and Functions

13.2 Exponential Functions

13.3 Logarithmic Functions

13.4 Properties of Logarithms

13.5 Logarithmic and Exponential Equations

Appendix A

Appendix A.1 Determinants and Cramer’s Rule

Intermediate Algebra

NEW


INTERMEDIATE ALGEBRA

Third Edition




2011 (January 2010) \ Hardcover

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.


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.


DEVELOPMENTAL MATHEMATICS


Chapter 1: Review of Basic Algebraic Concepts

1.1 Sets of Numbers and Interval Notation

1.2 Operations on Real Numbers

1.3 Simplifying Expressions

1.4 Linear Equations in One Variable

1.5 Applications of Linear Equations in One Variable

1.6 Literal Equations and Applications to Geometry

1.7 Linear Inequalities in One Variable

1.8 Properties of Integer Exponents and Scientific Notation

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Test

Chapter 2: Linear Equations in Two Variables

2.1 The Rectangular Coordinate System and Midpoint Formula

2.2 Linear Equations in Two Variables

2.3 Slope of a Line

2.4 Equations of a Line

2.5 Applications of Linear Equations and Graphing

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Test

Cumulative Review Exercises, Chapters 1 – 2

Chapter 3: Systems of Linear Equations

3.1 Solving Systems of Linear Equations by Graphing

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

3.7 Determinants and Cramer’s Rule

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Test

Cumulative Review Exercises, Chapters 1 – 3

Chapter 4: Introduction to Relations and Functions

4.1 Introduction to Relations

4.2 Introduction to Functions

4.3 Graphs of Functions

4.4 Variation

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Test

Cumulative Review Exercises, Chapters 1 – 4

Chapter 5:Polynomials

5.1 Addition and Subtraction of Polynomials and Polynomial Functions

5.2 Multiplication of Polynomials

5.3 Division of Polynomials

Problem Recognition Exercises – Operations on Polynomials

5.4 Greatest Common Factor and Factoring by Grouping

5.5 Factoring Trinomials

5.6 Factoring Binomials

5.7 Additional Factoring Strategies

5.8 Solving Equations by Using the Zero Product Rule

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Test

Cumulative Review Exercises, Chapters 1 – 5

Chapter 6:Rational Expressions and Rational Equations

6.1 Rational Expressions and Rational Functions

6.2 Multiplication and Division of Rational Expressions

6.3 Addition and Subtraction of Rational Expressions

6.4 Complex Fractions

Problem Recognition Exercises – Operations on Rational Expressions

6.5 Rational Equations

6.6 Applications of Rational Equations and Proportions

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Test

Cumulative Review Exercises, Chapters 1 – 6

Chapter 7: Radicals and Complex Numbers

7.1 Definition of an nth Root

7.2 Rational Exponents

7.3 Simplifying Radical Expressions

7.4 Addition and Subtraction of Radicals

7.5 Multiplication of Radicals

7.6 Rationalization

7.7 Radical Equations

7.8 Complex Numbers

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Test

Chapter 8: Quadratic Equations and Functions

8.1 Square Root Property and Completing the Square

8.2 Quadratic Formula

8.3 Equations in Quadratic Form

8.4 Graphs of Quadratic Functions

8.5 Vertex of a Parabola and Applications

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Test

Cumulative Review Exercises, Chapters 1 - 8

Chapter 9: More Equations and Inequalities

9.1 Compound Inequalities

9.2 Polynomial and Rational Inequalities

9.3 Absolute Value Equations

9.4 Absolute Value Inequalities

Problem Recognition – Equations and Inequalities

9.5 Linear Inequalities in Two Variables

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Test

Cumulative Review Exercises, Chapters 1 - 9

Chapter 10: Exponential and Logarithmic Functions

10.1 Algebra and Composition of Functions

10.2 Inverse Functions

10.3 Exponential Functions

10.4 Logarithmic Functions

10.5 Properties of Logarithms

10.6 The Irrational Number e

Problem Recognition – Logarithmic and Exponential Forms

10.7 Logarithmic and Exponential Equations

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Test

Cumulative Review Exercises, Chapters 1 - 10

Chapter 11: Conic Sections

11.1 Distance Formula and Circles

11.2 More on the Parabola

11.3 The Ellipse and Hyperbola

11.4 Nonlinear Systems of Equations in Two Variables

11.5 Nonlinear Inequalities and Systems of Inequalities

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Test

Cumulative Review Exercises, Chapters 1 – 11

Appendix

A.1 Binomial Expansions

A.2 Sequences and Series

A.3 Arithmetic and Geometric Sequences and Series


DEVELOPMENTAL MATHEMATICS

NEW


INTERMEDIATE ALGEBRA

Second Edition




2010 (January 2009) / Softcover / 992 pages

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-



Problem Recognition Exercises - These exercise sets are designed

to helop students learn to recognize the difference between

types of problems which appear to be similar at first, but indeed are

different and require different techniques to solve.

Improved Worked Out Solutions - Many multi-part sets and examples

have been split up to show to make viewing the solutions easier.

Engaging Chapter Openers - Now each chapter includes an

engaging and fun puzzle for students to review and/or learn concepts

from that chapter.

References to Classroom Exercises -- Not only does the Annotated

Instructor’s Edition uniquely refer to the Classroom Activities,

but now it references classroom exercises for each example in the

text. These exercises are highlighted in the Practice Set at the end

of each section. Should an instructor choose to present all of these

highlighted exercises, all of the objectives of that particular section

will have been covered.

Group Activities -- Optional Group Activities have been added

to the end of each chapter.


Chapter 1 Review of Basic Algebraic Concepts

1.1 Sets of Number and Interval Notation

1.2 Operation on Real Numbers

1.3 Simplifying Expressions

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

Expressions and Equations

1.5 Applications of Linear Equations in One Variable

1.6 Literal Equations and Applications to Geometry

1.7 Linear Inequalities in One Variable

1.8 Properties of Integer Exponents and Scientific Notation

Chapter 2 Graphing Linear Equations and Functions

2.1 Linear Equations in Two Variables

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

2.5 Introduction to Relations

2.6 Introduction to Functions

2.7 Graphs of Basic Functions

Chapter 3 Systems of Linear Equations

3.1 Solving Systems of Linear Equations by Graphing

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.

4.2 Multiplication of Polynomials

4.3 Division of Polynomials--Problem Recognition Exercises: Operations

on Polynomials

4.4 Greatest Common Factor and Factoring by Grouping

4.5 Factoring Trinomials

4.6 Factoring Binomials

4.7 Additional Factoring Strategies

4.8 Solving Equations by Using the Zero Product Rule

Chapter 5 Rational Expressions and Rational Equations

5.1 Rational Expressions and Rational Functions

5.2 Multiplication and Division of Rational Expressions

5.3 Addition and Subtraction of Rational Expressions

5.4 Complex Fractions--Problem Recognition Exercises: Simplifying

Rational Expressions

5.5 Solving Rational Equations--Problem Recognition Exercises:

Rational Expressions and Equations

5.6 Applications of Rational Equations and Proportions

5.7 Variation

Chapter 6 Radicals and Complex Numbers

6.1 Definition of an nth-Root

6.2 Rational Exponents

6.3 Simplifying Radical Expressions

6.4 Addition and Subtraction of Radicals

6.5 Multiplication of Radicals--Problem Recognition Exercises: Operations

on Radical Expressions

6.6 Rationalization

6.7 Solving Radical Equations

6.8 Complex Numbers

Chapter 7 Quadratic Equations and Functions

7.1 Square Root Property and Completing the Square

7.2 Quadratic Formula

7.3 Equations in Quadratic Form--Problem Recognition Exercises:

Recognizing Equation Types

7.4 Graphs of Quadratic Functions

7.5 Applications of Quadratic Functions and Modeling

Chapter 8 More Equations and Inequalities

8.1 Compound Inequalities

8.2 Polynomial and Rational Inequalities

8.3 Absolute Value Equations

8.4 Absolute Value Inequalities--Problem Recognition Exercises:

Equations and Inequalities

8.5 Linear Inequalities in Two Variables

Chapter 9 Exponential and Logarithmic Functions

9.1 Algebra and Composition of Functions

9.2 Inverse Functions

9.3 Exponential Functions

9.4 Logarithmic Functions

9.5 Properties of Logarithms

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


DEVELOPMENTAL MATHEMATICS

10.4 Nonlinear Systems of Equations in Two Variables

10.5 Nonlinear Inequalities and System if Inequalities

Additional Topics Appendix

A.1 Binomial Expansions

A.2 Determinants and Cramer’s Rule

A.3 Sequences and Series

A.4 Arithmetic and Geometric Sequences and Series

INTERMEDIATE ALGEBRA

Third Edition



2009 / Paper / 960 pages

ISBN: 9780077224806


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.


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

Chapter 2: Linear Equations and Inequalities

2.1 Linear Equations in One Variable

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

3.4 Linear Inequalities in Two Variables

3.5 Introduction to Functions

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

4.4 Systems of Linear Inequalities

Chapter 5: Polynomials

5.1 Polynomials: Addition and Subtraction

5.2 Multiplication of Polynomials

5.3 The Greatest Common Factor and Factoring by Grouping

5.4 Factoring Trinomials

5.5 Special Factoring

5.6 General Methods of Factoring

5.7 Solving Equations by Factoring: Applications

Chapter 6: Rational Expressions

6.1 Rational Expressions

6.2 Multiplication and Division of Rational Expressions

6.3 Addition and Subtraction of Rational Expressions

6.4 Complex Fractions

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

7.2 Simplifying Radicals

7.3 Operations with Radicals

7.4 Solving Equations Containing Radicals

7.5 Complex Numbers

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

9.1 Quadratic Functions and Their Graphs

9.2 Circles and Ellipses

9.3 Hyperbolas and Identification of Conics

9.4 Nonlinear Systems of Equations

9.5 Nonlinear Systems of Inequalities

Chapter 10: Functions-Inverse, Exponential, and Logarithmic

10.1 The Algebra of Functions

10.2 Inverse Functions

10.3 Exponential 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

INTERMEDIATE ALGEBRA

Sixth Edition


2009 \ 896 pages \ Hardcover

ISBN: 9780077224813


Intermediate 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

useful supplements, including McGraw-Hill’s online homework

management system, MathZone.


DEVELOPMENTAL MATHEMATICS


TO THE STUDENT

PREFACE

1 The Real Numbers

1.1 Sets

1.2 The Real Numbers

1.3 Operations on the Set of Real Numbers

1.4 Evaluating Expressions

1.5 Properties of the Real Numbers

1.6 Using the Properties

Chapter 1 Wrap-Up






2 Linear Equations and Inequalities in One Variable

2.1 Linear Equations in One Variable

2.2 Formulas and Functions

2.3 Applications

2.4 Inequalities

2.5 Compound Inequalities

2.6 Absolute Value Equations and Inequalities

Chapter 2 Wrap-Up







3 Linear Equations and Inequalities in Two Variables

3.1 Graphing Lines in the Coordinate Plane

3.2 Slope of a Line

3.3 Three Forms for the Equation of a Line

3.4 Linear Inequalities and Their Graphs

3.5 Functions and Relations

Chapter 3 Wrap-Up







4 Systems of Linear Equations

4.1 Solving Systems by Graphing and Substitution

4.2 The Addition Method

4.3 Systems of Linear Equations in Three Variables

4.4 Solving Linear Systems Using Matrices

4.5 Determinants and Cramer’s Rule

4.6 Linear Programming

Chapter 4 Wrap-Up







5 Exponents and Polynomials

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

5.8 Solving Equations by Factoring

Chapter 5 Wrap-Up







6 Rational Expressions and Functions

6.1 Properties of Rational Expressions and Functions

6.2 Multiplication and Division

6.3 Addition and Subtraction

6.4 Complex Fractions

6.5 Division of Polynomials

6.6 Solving Equations Involving Rational Expressions

6.7 Applications

Chapter 6 Wrap-Up







7 Radicals and Rational Exponents

7.1 Radicals

7.2 Rational Exponents

7.3 Adding, Subtracting, and Multiplying Radicals

7.4 Quotients, Powers, and Rationalizing Denominators

7.5 Solving Equations with Radicals and Exponents

7.6 Complex Numbers

Chapter 7 Wrap-Up







8 Quadratic Equations, Functions, and Inequalities

8.1 Factoring and Completing the Square

8.2 The Quadratic Formula

8.3 More on Quadratic Equations

8.4 Quadratic Functions and Their Graphs

8.5 Quadratic and Rational Inequalities

Chapter 8 Wrap-Up







9 Additional Function Topics

9.1 Graphs of Functions and Relations

9.2 Transformations of Graphs

9.3 Combining Functions

9.4 Inverse Functions

9.5 Variation

Chapter 9 Wrap-Up







10 Exponential and Logarithmic Functions

10.1 Exponential Functions and Their Applications

10.2 Logarithmic Functions and Their Applications

10.3 Properties of Logarithms

10.4 Solving Equations and Applications

Chapter 10 Wrap-Up







11 Nonlinear Systems and the Conic Sections

11.1 Nonlinear Systems of Equations


DEVELOPMENTAL MATHEMATICS

11.2 The Parabola

11.3 The Circle

11.4 The Ellipse and Hyperbola

11.5 Second-Degree Inequalities

Chapter 11 Wrap-Up







12 Sequences and Series

12.1 Sequences

12.2 Series

12.3 Arithmetic Sequences and Series

12.4 Geometric Sequences and Series

12.5 Binomial Expansions

Chapter 12 Wrap-Up







Appendix A

Answers to Selected Exercises

Index

SCHAUM’S EASY OUTLINE INTERMEDIATE

ALGEBRA



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!

SCHAUM’S OUTLINE OF INTERMEDIATE

ALGEBRA

Second Edition



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.

INVITATION TO PUBLISH






Visit McGraw-Hill Education (Asia)

Website: www.mheducation.asia


DEVELOPMENTAL MATHEMATICS

Algebra for College

Students

ALGEBRA FOR COLLEGE STUDENTS

Fifth Edition


2009 (January 2008) / 250 pages

ISBN: 9780077224844 (Mandatory Package)


Algebra for College Students, 5e 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


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 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.


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.


TO THE STUDENT

PREFACE

1 The Real Numbers

1.1 Sets

1.2 The Real Numbers

1.3 Operations on the Set of Real Numbers

1.4 Evaluating Expressions

1.5 Properties of the Real Numbers

1.6 Using the Properties

Chapter 1 Wrap-Up






2 Linear Equations and Inequalities in One Variable

2.1 Linear Equations in One Variable

2.2 Formulas and Functions

2.3 Applications

2.4 Inequalities

2.5 Compound Inequalities

2.6 Absolute Value Equations and Inequalities

Chapter 2 Wrap-Up







3 Linear Equations and Inequalities in Two Variables

3.1 Graphing Lines in the Coordinate Plane

3.2 Slope of a Line

3.3 Three Forms for the Equation of a Line

3.4 Linear Inequalities and Their Graphs

3.5 Functions and Relations

Chapter 3 Wrap-Up







4 Systems of Linear Equations

4.1 Solving Systems by Graphing and Substitution

4.2 The Addition Method

4.3 Systems of Linear Equations in Three Variables

4.4 Solving Linear Systems Using Matrices

4.5 Determinants and Cramer’s Rule

4.6 Linear Programming

Chapter 4 Wrap-Up







5 Exponents and Polynomials

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

5.8 Solving Equations by Factoring

Chapter 5 Wrap-Up







6 Rational Expressions and Functions

6.1 Properties of Rational Expressions and Functions

6.2 Multiplication and Division

6.3 Addition and Subtraction

6.4 Complex Fractions

6.5 Division of Polynomials

6.6 Solving Equations Involving Rational Expressions

6.7 Applications

Chapter 6 Wrap-Up







7 Radicals and Rational Exponents

7.1 Radicals

7.2 Rational Exponents

7.3 Adding, Subtracting, and Multiplying Radicals

7.4 Quotients, Powers, and Rationalizing Denominators

7.5 Solving Equations with Radicals and Exponents

7.6 Complex Numbers

Chapter 7 Wrap-Up







8 Quadratic Equations, Functions, and Inequalities


DEVELOPMENTAL MATHEMATICS

8.1 Factoring and Completing the Square

8.2 The Quadratic Formula

8.3 More on Quadratic Equations

8.4 Quadratic Functions and Their Graphs

8.5 Quadratic and Rational Inequalities

Chapter 8 Wrap-Up







9 Additional Function Topics

9.1 Graphs of Functions and Relations

9.2 Transformations of Graphs

9.3 Combining Functions

9.4 Inverse Functions

9.5 Variation

Chapter 9 Wrap-Up







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

Chapter 10 Wrap-Up







11 Exponential and Logarithmic Functions

11.1 Exponential Functions and Their Applications

11.2 Logarithmic Functions and Their Applications

11.3 Properties of Logarithms

11.4 Solving Equations and Applications

Chapter 11 Wrap-Up







12 Nonlinear Systems and the Conic Sections

12.1 Nonlinear Systems of Equations

12.2 The Parabola

12.3 The Circle

12.4 The Ellipse and Hyperbola

12.5 Second-Degree Inequalities

Chapter 12 Wrap-Up







13 Sequences and Series

13.1 Sequences

13.2 Series

13.3 Arithmetic Sequences and Series

13.4 Geometric Sequences and Series

13.5 Binomial Expansions

Chapter 13 Wrap-Up







14 Counting and Probability

14.1 Counting and Permutations

14.2 Combinations

14.3 Probability

Chapter 14 Wrap-Up






Appendix A

Answers to Selected Exercises

Index

SCHAUM’S OUTLINE OF MATHEMATICAL

HANDBOOK OF FORMULAS AND TABLES

Third Edition



2008 / Softcover / 312 pages

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.


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

7. Probability and Statistics


MATHEMATICS

SERVICE COURSES

Discrete Mathematics .........................................................................................40

Geometry ............................................................................................................35

Liberal Arts Mathematics ....................................................................................36

Mathematics for Elementary Teachers ...............................................................39

Professional References ....................................................................................42

Technical Mathematics .......................................................................................42


NEW TITLES

MATHEMATICS SERVICE COURSES

2011 Author ISBN-13 Page

Mathematics in Our World, 2e Sobecki 9780077356651 36

2010 Author ISBN-13 Page

Mathematics for Elementary Teachers: A Conceptual Approach, 8e Bennett 9780077297930 39

Mathematics for Elementary Teachers: An Activity Approach, 8e Bennett 9780077297947 39


MATHEMATICS SERVICE COURSES

Geometry

GEOMETRY WITH GEOMETRY EXPLORER


2005 / Hardcover with CDROM

ISBN: 9780073129907



1 Geometry and the Axiomatic Method

1.1 Early Origins of Geometry

1.2 Thales and Pythagoras

1.2.1 Thales

1.2.2 Pythagoras

1.3 Project 1--The Ratio Made of Gold

1.3.1 Golden Section

1.3.2 Golden Rectangles

1.4 The Rise of the Axiomatic Method

1.5 Properties of Axiomatic Systems

1.5.1 Consistency

1.5.2 Independence

1.5.3 Completeness

1.5.4 Gödel’s Incompleteness Theorem

1.6 Euclid’s Axiomatic Geometry

1.6.1 Euclid’s Postulates

1.7 Project 2--A Concrete Axiomatic System

2 Euclidean Geometry

2.1 Angles, Lines, and Parallels

2.2 Congruent Triangles and Pasch’s Axiom

2.3 Project 3--Special Points of a Triangle

2.3.1 Circumcenter

2.3.2 Orthocenter

2.3.3 Incenter

2.4 Measurement and Area in Eucliedean Geometry

2.4.1 Mini-Project--Area in Euclidean Geometry

2.4.2 Cevians and Areas

2.5 Similar Triangles

2.5.1 Mini-Project--Finding Heights

2.6 Circle Geometry

2.7 Project 4--Circle Inversion and Orthogonality

2.7.1 Orthogonal Circles Redux

3 Analytic Geometry

3.1 The Cartesian Coordinate System

3.2 Vector Geometry

3.3 Project 5--Bézier Curves

3.4 Angles in Coordinate Geometry

3.5 The Complex Plane

3.5.1 Polar Form

3.5.2 Complex Functions

3.5.3 Analytic Functions and Conformal Maps (Optional)

3.6 Birkhoff’s Axiomatic System for Analytic Geometry

4 Constructions

4.1 Euclidean Constructions

4.2 Project 6--Euclidean Eggs

4.3 Constructibility

4.4 Mini-Project--Origami Construction

5 Transformational Geometry

5.1 Euclidean Isometries

5.2 Reflections

5.2.1 Mini-Project--Isometries through Reflection

5.2.2 Reflection and Symmetry

5.3 Translations

5.3.1 Translational Symmetry

5.4 Rotations

5.4.1 Rotational Symmetry

5.5 Project 7--Quilts and Transformations

5.6 Glide Reflections

5.6.1 Glide Reflection Symmetry

5.7 Structure and Representation of Isometries

5.7.1 Matrix Form of Isometries

5.7.2 Compositions of Rotations and Translations

5.7.3 Compositions of Reflections and Glide Reflections

5.7.4 Isometries in Computer Graphics

5.7.5 Summary of Isometry Compositions

5.8 Project 8--Constructing Compositions

6 Symmetry

6.1 Finite Plane Symmetry Groups

6.2 Frieze Groups

6.3 Wallpaper Groups

6.4 Tiling the Plane

6.4.1 Escher

6.4.2 Regular Tessellations of the Plane

6.5 Project 9--Constructing Tessellations

7 Non-Euclidean Geometry

7.1 Background and History

7.2 Models of Hyperbolic Geometry

7.2.1 Poincaré Model

7.2.2 Mini-Project--The Klein Model

7.3 Basic Results in Hyperbolic Geometry

7.3.1 Parallels in Hyperbolic Geometry

7.3.2 Omega Points and Triangles

7.4 Project 10--The Saccheri Quadrilateral

7.5 Lambert Quadrilaterals and Triangles

7.5.1 Lambert Quadrilaterals

7.5.2 Triangles in Hyperbolic Geometry

7.6 Area in Hyperbolic Geometry

7.7 Project 11--Tiling the Hyperbolic Plane

7.8 Models and Isomorphism

8 Non-Euclidean Transformations

8.1 Möbius Transformations

8.1.1 Fixed Points and the Cross Ratio

8.1.2 Geometric Properties of Möbius Transformations

8.2 Isometries in the Poincaré Model

8.3 Isometries in the Klein Model

8.4 Mini-Project--The Upper Half-Plane Model

8.5 Weierstrass Model

8.6 Hyperbolic Calculation

8.6.1 Arclength of Parameterized Curves

8.6.2 Geodesics

8.6.3 The Angle of Parallelism

8.6.4 Right Triangles

8.6.5 Area

8.7 Project 12--Infinite Real Estate?

9 Fractal Geometry

9.1 The Search for a “Natural” Geometry

9.2 Self-Similarity

9.2.1 Sierpinski’s Triangle

9.2.2 Cantor Set

9.3 Similarity Dimension

9.4 Project 13--An Endlessly Beautiful Snowflake

9.5 Contraction Mappings and the Space of Fractals

9.6 Fractal Dimension

9.7 Project 14--IFS Ferns

9.8 Algorithmic Geometry

9.8.1 Turtle Geometry

9.9 Grammars and Productions

9.9.1 Space-filling Curves

9.10 Project 15--Words into Plants: The Geometry of Life

A Book I of Euclid’s Elements

A.1 Definitions

A.2 The Postulates (Axioms)

A.3 Common Notions

A.4 Propositions (Theorems)

B Brief Guide to Geometry Explorer

B.1 The Main Geometry Explorer Window

B.2 Selecting Objects

B.3 Active vs. Inactive Tools

B.4 Labels


MATHEMATICS SERVICE COURSES

B.5 Object Coloring

B.6 Online Help

B.7 Undo/Redo of Actions

B.8 Clearing and Resizing the Canvas

B.9 Saving Files as Images

B.10 Main Window Button Panels

B.10.1 Create Panel

B.10.2 Construct Panel

B.10.3 Transform Panel

B.11 Measurement in Geometry Explorer

B.11.1 Neutral Measurements

B.11.2 Euclidean-only Measurements

B.11.3 Hyperbolic-only Measurements

B.11.4 User Input Measurements

B.12 Using Tables

B.13 Using the Calculator

B.14 Hyperbolic Geometry

B.15 Analytic Geometry

B.16 Turtle Geometry

C Birkhoff’s Axioms for Euclidean Geometry

D Hilbert’s Axioms for Euclidean Geometry

E The 17 Wallpaper Groups

SCHAUM’S OUTLINE OF GEOMETRY

Fourth Edition


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


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

SCHAUM’S EASY OUTLINES: GEOMETRY



2001 / 144 pages

ISBN: 9780071369732



Chapter 1: Lines, Angles, and Triangles.

Chapter 2: Deductive Reasoning.

Chapter 3: Congruent Triangles.

Chapter 4: Parallel Lines, Distances, and Angle Sums.

Chapter 5: Trapezoids and Parallelograms.

Chapter 6: Circles.

Chapter 7: Similarity.

Chapter 8: Areas.

Chapter 9: Regular Polygons and the Circle.

Chapter 10: Constructions.

Liberal Arts Mathematics

NEW


MATHEMATICS IN OUR

WORLD

Second Edition




2011 (January 2010)

ISBN: 9780077356651


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.


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


MATHEMATICS SERVICE COURSES

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.


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 2 Review

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 3 Review

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 4 Review

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 5 Review

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 6 Review

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 7 Review

Chapter 8: Consumer Mathematics

8-1 Percents

8-2 Simple Interest

8-3 Compound Interest

8-4 Installment Buying

8-5 Home Ownership

8-6 Stocks and Bonds

Chapter 8 Review

Chapter 9: Measurement

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 9 Review

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 10 Review

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 11 Review

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 12 Review

Chapter 13: Other Mathematical Systems

13-1 Mathematical Systems and Groups

13-2 Clock Arithmetic

13-3 Modular Systems

Chapter 13 Review

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 14 Review

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

Chapter 15 Review


MATHEMATICS SERVICE COURSES

MATHEMATICS IN OUR WORLD WITH

MATHZONE


2005 / Hardcover with access card / 840 pages

ISBN: 9780073311821




One Problem Solving

1-1 The Nature of Mathematical Reasoning

1-2 Problem Solving

1-3 Estimation

Two 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

Three Logic

3-1 Statements

3-2 Truth Tables

3-3 Types of Statements

3-4 Arguments

3-5 Euler Circles

Four Numeration Systems

4-1 Early and Modern Numeration Systems

4-2 Base Number Systems

4-3 Operations in Base Numbers

Five 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

Six Other Mathematical Systems

6-1 Clock Arithmetic

6-2 Modular Systems

6-3 Mathematical Systems without Numbers

Seven Topics in Algebra

7-1 Fundamental Concepts of Algebra

7-2 Solving Linear Equations

7-3 Applications of Linear Equations

7-4 Solving Linear Inequalities

7-5 Ratio, Proportion, and Variation

7-6 Solving Quadratic Equations

Eight Additional Topics in Algebra

8-1 The Rectangular Coordinate System and the Line

8-2 Systems of Linear Equations

8-3 Systems of Linear Inequalities

8-4 Linear Programming

8-5 Functions

Nine Consumer Mathematics

9-1 Percent

9-2 Interest

9-3 Installment Buying

9-4 Home Ownership

9-5 Markup and Markdown

Ten Geometry

10-1 Points, Lines, Planes, and Angles

10-2 Triangles

10-3 Polygons and Perimeter

10-4 Areas of Polygons and the Circle

10-5 Surface Area and Volume

10-6 Right Triangle Trigonometry

10-7 Networks

Eleven Probability and Counting Techniques

11-1 Basic Concepts of Probability

11-2 Tree Diagrams, Tables, and Sample Spaces

11-3 Odds and Expectation

11-4 The Addition Rules for Probability

11-5 The Multiplication Rules and Conditional Probability

11-6 The Fundamental Counting Rule and Permutations

11-7 Combinations

11-8 Probability Using Permutations and Combinations

Twelve 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

Thirteen Voting Methods

13-1 Preference Tables and the Plurality Method

13-2 The Borda Count Method and the Plurality-with-Elimination

Method

13-3 The Pairwise Comparison Method and Approval Voting

Appendix A Measurement

Appendix B Trigonometric Ratios

Appendix C Area Under the Standard Normal Distribution

Appendix D Significan Values for the Correlation Coefficient

Appendix E Using the Ti83+ Graphing Calculator

International Edition

APPLIED MATHEMATICS FOR BUSINESS,

ECONOMICS AND THE SOCIAL SCIENCE

Fourth Edition


1993 / 1,056 pages / Softcover

ISBN: 9780070089020 (Out-of-Print)

ISBN: 9780071125802 [IE]


1 Some Preliminaries

2 Linear Equations

3 Systems of Linear Equations

4 Functions and Graphs

5 Linear Functionsand Applications

6 Quadratic and Polynomial Functions

7 Exponential and Logarithmic 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


MATHEMATICS SERVICE COURSES

Mathematics for

Elementary Teachers

NEW


International Edition

MATHEMATICS

FOR ELEMENTARY

TEACHERS:

A Conceptual Approach

Eighth Edition




2010 (January 2009) \ Package

ISBN: 9780077297930

ISBN: 9780071310024 (IE, with Manipulative Kit)


Overview: Albert B. Bennett, Jr. and L. Ted Nelson have presented

hundreds of workshops on how to give future teachers the conceptual

cessfully

teach elementary-school mathematics. The Eighth Edition

of Mathematics for Elementary Teachers: A Conceptual Approach

continues their innovative, time-tested approach: an emphasis on


visual aids, hands-on activities, problem-solving strategies and active

classroom participation. Special features in the text ensure 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. The text also incorporates references to the virtual

manipulative kit and other online resources that enhance the authors’

explanations and examples.


1 Problem Solving

1.1 Seeing and Extending Patterns with Pattern Blocks

1.2 Geometric Number Patterns with Color Tile

1.3 Solving Story Problems with Algebra Pieces

2 Sets, Functions, and Reasoning

2.1 Sorting and Classifying with Attribute Pieces

2.2 Slope and Linear Functions on Geoboards

2.3 Logic Problems for Cooperative Learning Groups

3 Whole Numbers

3.1 Models for Numeration with Multibase Pieces

3.2 Adding and Subtracting with Multibase Pieces

3.3 Multiplying with Base-Ten Pieces

3.4 Dividing with Base-Ten Pieces

4 Number Theory

4.1 Models for Even Numbers, Odd Numbers, Factors, and Primes

4.2 Models for Greatest Common Factors and Least Common Multiple

5 Integers and Fractions

5.1 Black and Red Tile Model for Integers

5.2 Fractions Bar Model for Equality and Inequality

5.3 Computing with Fraction Bars

6 Decimals: Rational and Irrational

6.1 Decimal Squares Model

6.2 Operations with Decimal Squares

6.3 A Model for Introducing Percent

6.4 Irrational Numbers on the Geoboard

7 Statistics

7.1 Collecting and Graphing Data

7.2 Analyzing Data, Sampling, and Simulation

7.3 Statistical Distributions: Observations and Applicatons

8 Probability

8.1 Probability Experiments

8.2 Multistage Probability Experiments

9 Geometric Figures

9.1 Figures on Rectangular and Circular Geoboards

9.2 Regular and Semiregular Tessellations

9.3 Models for Regular and Semiregular Polyhedra

9.4 Creating Symmetric Figures: Pattern Blocks and Paper Folding

10 Measurement

10.1 Measuring the Metric Units

10.2 Areas on Geoboards

10.3 Models for Volume and Surface Area

11 Motions in Geometry

11.1 Locating Sets of Points in the Plane

11.2 Drawing Escher-Type Tessellations

11.3 Devises for Indirect Activities

References for Research Statements by Chapters

Answers to Selected Activities

Answers to Odd-Numbered Exercises, Problems and Chapter Tests

NEW


MATHEMATICS FOR

ELEMENTARY TEACHERS:

An Activity Approach

Eighth Edition




2010 (January 2009) \ Softcover

ISBN: 9780077297947


This book is designed for a mathematics for elementary school

teachers course where instructors choose to focus on and/or take

an activities approach to learning. It provides inductive activities for

prospective elementary school teachers and incorporates the use

of physical models, manipulatives, and visual images to develop

concepts and encourage higher-level thinking. This text contains an

activity set that corresponds to each section of the companion text,

Mathematics for Elementary Teachers: A Conceptual Approach which

is also by Bennett/Nelson. The Activities Approach text can be used

independently or along with its companion volume. The authors are

pleased to welcome Laurie Burton, PhD, Western Oregon University

to this edition of Mathematics for Elementary Teachers: An Activity

Approach.


1 Problem Solving

1.1 Seeing and Extending Patterns with Pattern Blocks

1.2 Geometric Number Patterns with Color Tile

1.3 Solving Story Problems with Algebra Pieces

2 Sets, Functions, and Reasoning


MATHEMATICS SERVICE COURSES

2.1 Sorting and Classifying with Attribute Pieces

2.2 Slope and Linear Functions on Geoboards

2.3 Logic Problems for Cooperative Learning Groups

3 Whole Numbers

3.1 Models for Numeration with Multibase Pieces

3.2 Adding and Subtracting with Multibase Pieces

3.3 Multiplying with Base-Ten Pieces

3.4 Dividing with Base-Ten Pieces

4 Number Theory

4.1 Models for Even Numbers, Odd Numbers, Factors, and Primes

4.2 Models for Greatest Common Factors and Least Common Multiple

5 Integers and Fractions

5.1 Black and Red Tile Model for Integers

5.2 Fractions Bar Model for Equality and Inequality

5.3 Computing with Fraction Bars

6 Decimals: Rational and Irrational

6.1 Decimal Squares Model

6.2 Operations with Decimal Squares

6.3 A Model for Introducing Percent

6.4 Irrational Numbers on the Geoboard

7 Statistics

7.1 Collecting and Graphing Data

7.2 Analyzing Data, Sampling, and Simulation

7.3 Statistical Distributions: Observations and Applicatons

8 Probability

8.1 Probability Experiments

8.2 Multistage Probability Experiments

9 Geometric Figures

9.1 Figures on Rectangular and Circular Geoboards

9.2 Regular and Semiregular Tessellations

9.3 Models for Regular and Semiregular Polyhedra

9.4 Creating Symmetric Figures: Pattern Blocks and Paper Folding

10 Measurement

10.1 Measuring the Metric Units

10.2 Areas on Geoboards

10.3 Models for Volume and Surface Area

11 Motions in Geometry

11.1 Locating Sets of Points in the Plane

11.2 Drawing Escher-Type Tessellations

11.3 Devises for Indirect Activities

Answers to Selected Activities

Credits

Index

Material Cards

NCTM Standards

Discrete Mathematics

International Edition

DISCRETE MATHEMATICS AND ITS

APPLICATIONS

Sixth Edition


2007 (January 2006) / Hardcover with Access card

ISBN: 9780073229720 (with MathZone)

ISBN: 9780073312712 (with Math Zone Kit) - Out-of-Print

ISBN: 9780071244749 [IE]



Preface. The Companion Website. To the Student.

1 The Foundations: Logic and Proof, Sets, and Functions

1.1 Logic

1.2 Propositional Equivalences

1.3 Predicates and Quantifiers

1.4 Nested Quantifiers

1.5 Methods of Proof

1.6 Sets

1.7 Set Operations

1.8 Functions

End-of-Chapter Material.

2 The Fundamentals: Algorithms, the Integers, and Matrices

2.1 Algorithms

2.2 The Growth of Functions

2.3 Complexity of Algorithms

2.4 The Integers and Division

2.5 Integers and Algorithms

2.6 Applications of Number Theory

2.7 Matrices

End-of-Chapter Material.

3 Mathematical Reasoning, Induction, and Recursion

3.1 Proof Strategy

3.2 Sequences and Summations

3.3 Mathematical Induction

3.4 Recursive Definitions and Structural Induction

3.5 Recursive Algorithms

3.6 Program Correctness

End-of-Chapter Material.

4 Counting

4.1 The Basics of Counting

4.2 The Pigeonhole Principle

4.3 Permutations and Combinations

4.4 Binomial Coefficients

4.5 Generalized Permutations and Combinations

4.6 Generating Permutations and Combinations.

End-of-Chapter Material.

5 Discrete Probability

5.1 An Introduction to Discrete Probability

5.2 Probability Theory

5.3 Expected Value and Variance.

End-of-Chapter Material.

6 Advanced Counting Techniques

6.1 Recurrence Relations

6.2 Solving Recurrence Relations

6.3 Divide-and-Conquer Algorithms and Recurrence Relations

6.4 Generating Functions

6.5 Inclusion-Exclusion

6.6 Applications of Inclusion-Exclusion

End-of-Chapter Material.

7 Relations

7.1 Relations and Their Properties


MATHEMATICS SERVICE COURSES

7.2 n-ary Relations and Their Applications

7.3 Representing Relations

7.4 Closures of Relations

7.5 Equivalence Relations

7.6 Partial Orderings

End-of-Chapter Material.

8 Graphs

8.1 Introduction to Graphs

8.2 Graph Terminology

8.3 Representing Graphs and Graph Isomorphism

8.4 Connectivity

8.5 Euler and Hamilton Paths

8.6 Shortest-Path Problems

8.7 Planar Graphs

8.8 Graph Coloring

End-of-Chapter Material.

9 Trees

9.1 Introduction to Trees

9.2 Applications of Trees

9.3 Tree Traversal

9.4 Spanning Trees

9.5 Minimum Spanning Trees

End-of-Chapter Material

10 Boolean Algebra

10.1 Boolean Functions

10.2 Representing Boolean Functions

10.3 Logic Gates

10.4 Minimization of Circuits

End-of-Chapter Material.

11 Modeling Computation

11.1 Languages and Grammars

11.2 Finite-State Machines with Output

11.3 Finite-State Machines with No Output

11.4 Language Recognition

11.5 Turing Machines End-of-Chapter Material

Appendixes

A.1 Exponential and Logarithmic Functions

A.2 Pseudocode Suggested Readings

Answers to Odd-Numbered Exercises

Photo Credits

Index of Biographies

Index

International Edition

DISCRETE MATHEMATICS BY EXAMPLE


2002 / 450 pages

ISBN: 9780077098407

ISBN: 9780071229142 [IE]



1 Introduction.

2 Numbers.

3 Propositional logic.

4 Set theory.

5 Boolean algebra.

6 Typed set theory.

7 Predicate logic.

8 Relations.

9 Functions.

10 Sequences.

11 Induction.

12 Graph theory.

13 Combinatorics.

14 Modelling.

15 Analysis.

SCHAUM’S OUTLINE OF DISCRETE

MATHEMATICS

3rd Edition



2009 (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.


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

International Edition

SCHAUM’S 2,000 SOLVED PROBLEMS IN

DISCRETE MATHEMATICS


1992 / 412 pages

ISBN: 9780070380318

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




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.


MATHEMATICS SERVICE COURSES

Technical Mathematics

Professional References

MATHEMATICS FOR TECHNICIANS

Sixth Edition


2007 / Softcover / 446 pages

ISBN: 9780070131651


Mathematics for Technicians remains the leading Australian text for

students of stage one courses in mathematics, including Engineering

Maths A and Engineering Maths B. The new thoroughly revised

sixth edition incorporates the successful building block approach of

the previous edition, and includes banks of exercises and worked

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

Subjects covered include basic arithmetic, algebra, geometry

and trigonometry, logarithms and exponential functions, functions

and their graphs (circle, parabola, hyperbola), trigonometrical functions

and their graphs, phase angles and introductions to vectors,

determinants and matrices. A chapter on rotational equilibrium and

elementary frame analysis has been introduced for Civil Engineering

students. Answers to questions in the text have been relocated from

the CD to the back of the book for ease of use.. CD-Rom Continuing

the successful innovation of the previous edition, the CD-Rom

includes scores of extra exercises and questions for each chapter.

SUPERSYMMETRY DEMYSTIFIED


2010 / Softcover / 496 pages

ISBN: 9780071636414


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

research in particle physics, including superstring theory. The book

ing

on them as the chapters progress. Hundreds of worked equations

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



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








Visit McGraw-Hill Education

Website: www.mheducation.asia

SCHAUM’S OUTLINE OF BASIC BUSINESS

MATHEMATICS

Second Edition


2009 / Softcover / 272 pages

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.


Review of Arithmetic.

Ratio, Proportion, and Percent.

Payroll.

Depreciation.


MATHEMATICS SERVICE COURSES

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

Second Edition



2009 / Softcover / 504 pages

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.


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

17. Conic Sections

18. Numbering Systems

19. Arithmetic Operations in a Computer

20. Counting Methods

21. Probability and Odds

22. Statistics

MASTERING TECHNICAL MATHEMATICS

Third Edition


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.


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

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


MATHEMATICS SERVICE COURSES

SCHAUM’S OUTLINE OF BEGINNING FINITE

MATHEMATICS



2005 / Softcover / 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


and 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.

International Edition

SCHAUM’S OUTLINE OF INTRODUCTION

TO MATHEMATICAL ECONOMICS

Third Edition


2001 / 523 pages

ISBN: 9780071358965

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



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 MATHEMATICAL

METHODS FOR BUSINESS AND

ECONOMICS


1993 / 320 pages

ISBN: 9780070176973



Review.

Equations and Graphs.

Functions.

Systems of Equations.

Linear (or Matrix) Algebra.

Solving Linear Equations with Matrix Algebra.

Linear Programming: Using Graphs.

Linear Programming: The Simplex Algorithm and the Dual.

Differential Calculus: The Derivative and the Rules of Differentiation.

Differential Calculus: Uses of the Derivative.

Exponential and Logarithmic Functions.

Integral Calculus.

Calculus of Multivariable Functions.

Index.


PRECALCULUS

College Algebra ..................................................................................................47

College Algebra with Trigonometry .....................................................................53

Precalculus .........................................................................................................56

Trigonometry ......................................................................................................51


NEW TITLES

PRECALCULUS

2011 Author ISBN-13 Page

College Algebra, 9e Barnett 9780077350161 47

College Algebra with Trigonometry, 9e Barnett 9780077350109 53

PreCalculus, 7e Barnett 9780077349912 56

Trigonometry, 2e Coburn 9780077349974 51

PRECALCULUS

2010 Author ISBN-13 Page

Algebra & Trigonometry, 2e Coburn 9780077276515 54

College Algebra, 2e Coburn 9780077276492 48

College Algebra Essentials, 2e Coburn 9780077297909 49

PreCalculus, 2e Coburn 9780077276508 57


PRECALCULUS

NEW

College Algebra


COLLEGE ALGEBRA

Ninth Edition



2011 (January 2010) / Hardcover

ISBN: 9780077350161


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.


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

CHAPTER 1: EQUATIONS AND INEQUALITIES

1-1 Linear Equations and Applications

1-2 Linear Inequalities

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 1 Review

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 2 Review

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

Chapter 3 Review

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 4 Review

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

Chapter 5 Review

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 6 Review

CHAPTER 7: SYSTEMS OF EQUATIONS AND INEQUALITIES;

MATRICES

7-1 Systems of Linear Equations

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

7-8 Linear Programming

Chapter 7 Review

CHAPTER 8: SEQUENCES AND SERIES

8-1 Sequences and Series

8-2 Mathematical Induction

8-3 Arithmetic and Geometric Sequences

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

Chapter 8 Review

6, 7, & 8 Cumulative Review Exercises

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


PRECALCULUS

NEW


International Edition

COLLEGE ALGEBRA

Second Edition



2010 (January 2009) / Softcover

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

dents

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.


Interior Design - The trim size of the book has been increased

to provide more white space on the page, improve readability, and

decrease the length of the book. The font size has been increased

throughout. The size of graphs and diagrams has been increased

where necessary.

Updated Examples - Titles have been added to Examples and

the Examples have been scrutinized for clarity, length, and relevance

to current topics. “Overlapping” Examples have been removed.

Learning Objectives - These are clearly tied to sub-sections in the

text. Margin “checkpoints” throughout each section let students know

when a specific learning objective has been covered and reinforces

the use of correct mathematical terms.

Suggested Homework - A list of suggested homework assignments

has been added to each exercise section in the Annotated

Instructor’s Edition to provide instructors with guidelines for developing

core, standard, extended, and in-depth assignments.

Organizational Changes - Coverage of absolute value equations

and inequalities has been added to Chapter 1. Chapters 2, 3, and

4 have been significantly reorganized based on reviewer feedback.

Coverage of circles is now introduced in Chapter 2 with coverage of

the mid-point and distance formulas. Variation is now covered after

polynomial and rational functions. Coverage of one-to-one and inverse

functions has moved to Chapter 4 on Exponents and Logarithms.

Systems and Matrices are now covered in two separate chapters.


Chapter R: A Review of Basic Concepts and Skills

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

1-4 Complex Numbers

1-5 Solving Quadratic Equations

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

Chapter 3: Polynomial and Rational 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

3-6 Additional Insights into Rational Functions

3-7 Polynomial and Rational Inequalities

3-8 Variation: Function Models in Action

Chapter 4: Exponential and Logarithmic Functions

4-1 One-to-One and Inverse Functions

4-2 Exponential 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

Chapter 5: Systems of Equations and Inequalities

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

Chapter 6: Matrices and Matrix Applications

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

Chapter 8: Additional Topics in Algebra

8-1 Sequences and Series

8-2 Arithmetic Sequences

8-3 Geometric Sequences

8-4 Mathematical Induction

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


PRECALCULUS

NEW


COLLEGE ALGEBRA

ESSENTIALS

Second Edition



2010 (January 2009) / Hardcover

ISBN: 9780077297909


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 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.


Interior Design - The trim size of the book has been increased

to provide more white space on the page, improve readability, and

decrease the length of the book. The font size has been increased

throughout. The size of graphs and diagrams has been increased

where necessary.

Updated Examples - Titles have been added to Examples and

the Examples have been scrutinized for clarity, length, and relevance

to current topics. “Overlapping” Examples have been removed.

Learning Objectives - These are clearly tied to sub-sections in the

text. Margin “checkpoints” throughout each section let students know

when a specific learning objective has been covered and reinforces

the use of correct mathematical terms.

Suggested Homework - A list of suggested homework assignments

has been added to each exercise section in the Annotated

Instructor’s Edition to provide instructors with guidelines for developing

core, standard, extended, and in-depth assignments.

Organizational Changes - Coverage of absolute value equations

and inequalities has been added to Chapter 1. Chapters 2, 3, and

4 have been significantly reorganized based on reviewer feedback.

Coverage of circles is now introduced in Chapter 2 with coverage of

the mid-point and distance formulas. Variation is now covered after

polynomial and rational functions. Coverage of one-to-one and inverse

functions has moved to Chapter 4 on Exponents and Logarithms.

Systems and Matrices are now covered in two separate chapters.


Chapter R: A Review of Basic Concepts and Skills

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

1-4 Complex Numbers

1-5 Solving Quadratic Equations

1-6 Solving Other Types of Equations

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

Chapter 3: Polynomial and Rational 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

3-6 Additional Insights into Rational Functions

3-7 Polynomial and Rational Inequalities

3-8 Variation: Function Models in Action

Chapter 4: Exponential and Logarithmic Functions

4-1 One-to-One and Inverse Functions

4-2 Exponential 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

Chapter 5: Systems of Equations and Inequalities

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

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 from College Algebra


PRECALCULUS

COLLEGE ALGEBRA: GRAPHS AND

MODELS

Third Edition




2009 (February 2008)

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.


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

1-6 Inverse Functions

Chapter 1 Review

Chapter 1 Group Activity: Mathematical Modeling–Choosing a Long

Distance Calling Plan

CHAPTER 2 MODELING WITH LINEAR AND QUADRATIC FUNC-

TIONS

2-1 Linear Functions

2-2 Linear Equations and Models

2-3 Quadratic Functions

2-4 Complex Numbers

2-5 Quadratic Equations and Models

2-6 Additional Equation Solving Techniques

2-7 Solving Inequalities

Chapter 2 Review

Chapter 2 Group Activity: Mathematical Modeling in Population

Studies

Cumulative Review Exercise for Chapters 1 and 2

CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS

3-1 Polynomial Functions And Models

3-2 Polynomial Division

3-3 Real Zeros and Polynomial Inequalities

3-4 Complex Zeros and Rational Zeros of Polynomials

3-5 Rational Functions and Inequalities

3-6 Variation and Modeling

Chapter 3 Review

Chapter 3 Group Activity: Interpolating Polynomials

CHAPTER 4 MODELING WITH EXPONENTIAL AND LOGARITHMIC

FUNCTIONS

4-1 Exponential Functions

4-2 Exponential Models

4-3 Logarithmic Functions

4-4 Logarithmic Models

4-5 Exponential and Logarithmic Equations

Chapter 4 Review

Cumulative Review Chapters 3 and 4

Chapter 4 Group Activity: Comparing Regression Models

Cumulative Review Exercise for Chapters 3 and 4

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

5-3 Systems of Linear Inequalities

5-4 Linear Programming

Chapter 5 Review

Chapter 5 Group Activity: Modeling with Systems of Equations

CHAPTER 6 MATRICES AND DETERMINANTS

6-1 Matrix Solutions to Linear Systems

6-2 Matrix Operations

6-3 Inverse of a Square Matrix

6-4 Matrix Equations and Systems of Linear Equations

6-5 Determinants

6-6 Properties of Determinants

6-7 Determinants and Cramer’s Rule

Chapter 6 Review

Chapter 6 Group Activity: Using Matrices to Find Cost, Revenue,

and Profit

Cumulative Review Exercise for Chapters 5 and 6

CHAPTER 7 SEQUENCES, INDUCTION, PROBABILITY

7-1 Sequences and Series

7-2 Mathematical Induction

7-3 Arithmetic and Geometric Sequences

7-4 Multiplication Principle, Permutations, and Combinations

7-5 Sample Spaces and Probability

7-6 Binomial Formula

Chapter 7 Review

Chapter 7 Group Activity: Sequences Specified by Recursion Formulas

CHAPTER 8 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY

8-1 Conic Sections; Parabola

8-2 Ellipse

8-3 Hyperbola

8-4 Systems of Nonlinear Equations

8-5 Rotation of Axes

Chapter 8 Review

Chapter 8 Group Activity: Focal Chords

Cumulative Review Exercise for Chapters 7 and 8

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

SCHAUM’S OUTLINE OF COLLEGE

ALGEBRA

Third Edition



2009 (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

Trigonometry


TRIGONOMETRY

Second Edition



SCHAUM’S EASY OUTLINE: COLLEGE

ALGEBRA



2000 / 160 pages

ISBN: 9780070527096



Functions, Limits, Continuity.

Fundamental Differentiation.

Implicit Differentiation.

Tangents and Normals.

Maxima and Minima.

Differentiating for Special Functions.

Implicit Differentiating.

The Law of the Mean.

Indeterminate Forms.

Differentials.

Curve Tracing.

Fundamental Integration.

Applications of Indefinite Integrals.

The Definite Integral.

Plane Areas of Integration.

Exponential and Logarithmic Functions.

Exponential Growth and Decay.

Improper Integrals.

2011 (January 2010) / Hardcover

ISBN: 9780077349974


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 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 course


students across the country, 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.


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.


PRECALCULUS

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.


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

Mid-Chapter Check

RBC: The Area of a Triangle

2.3 Applications of Static Trigonometry

2.4 Extending Beyond Acute Angles

Summary/Concept Rev, Mixed Rev, Practice Test

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

Mid-Chapter Check

RBC: More on Radians

3.3 The Unit Circle

3.4 The Trigonometry of Real Numbers

Summary/Concept Rev, Mixed Rev, Practice Test

Calc Exploration and Discovery: Signs, Quadrants and Reference

Arcs

SCS: Trigonometry of the Real Numbers and the Wrapping Function

Cumulative Review 1 - 3

Chapter 4: Trigonometric Graphs and Models

4.1 Graphs of Sine and Cosine Functions

4.2 Graphs of Cosecant, Secant, Tangent and Cotangent

Functions

Mid-Chapter Check

RBC: Trigonometric Potpourri

4.3 Transformations of Trigonometric Graphs

4.4 Trigonometric Applications and Models

Summary/Concept Rev, Mixed Rev, Practice Test

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

Summary/Concept Rev, Mixed Rev, Practice Test

Calc Exploration and Discovery

SCS

Cumulative Review 1 - 5

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

Summary/Concept Rev, Mixed Rev, Practice Test

Calc Exploration and Discovery

SCS: Trigonometric Equations and Inequalities

Cumulative Review 1 - 6

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

Summary/Concept Rev, Mixed Rev, Practice Test

Calc Exploration and Discovery

SCS

Cumulative Review 1 - 7

Chapter 8: Trigonometric Connections to Algebra

8.1 Complex Numbers

8.2 Complex Numbers in Trigonometric Form

8.3 Demoivre’s Theorem and the nth Roots Theorem

Mid-Chapter Check

RBC

8.4 Polar Coordinates and Equations

8.5 Graphs of Polar Equations

8.6 Parametric Equations and Graphs

Summary/Concept Rev, Mixed Rev, Practice Test

Calc Exploration and Discovery

SCS

Cumulative Review 1 – 8

Appendices

A.1 Exponential and Logarithmic Functions

A.2 Review and Technology






SCHAUM’S OUTLINE OF TRIGONOMETRY

Fourth Edition



2009 (July 2008) / 211 pages

ISBN: 9780071543507


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 trigonometry

courses.


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


PRECALCULUS

College Algebra with

Trigonometry

NEW


International Edition

COLLEGE ALGEBRA WITH TRIGONOMETRY

Ninth Edition



2011 (January 2010)

ISBN: 9780077350109

ISBN: 9780071221757 [IE]


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.


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

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.


CHAPTER R: BASIC ALGEBRAIC OPERATIONS

R-1 Algebra and Real Numbers

R-2 Exponents and Radicals

R-3 Polynomials: Basic Operations and Factoring

R-4 Rational Expressions: Basic Operations

Chapter R Review

CHAPTER 1: EQUATIONS AND INEQUALITIES

1-1 Linear Equations and Applications

1-2 Linear Inequalities

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 1 Review

CHAPTER 2: GRAPHS

2-1 Rectangular Coordinates

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 2 Review

CHAPTER 3: FUNCTIONS

3-1 Functions

3-2 Graphing Functions

3-3 Transformations of Functions

3-3 Quadratic Functions

3-5 Combining Functions; Composition

3-6 Inverse Functions

Chapter 3 Group Activity: Mathematical Modeling - Choosing a Long-

Distance Calling Plan

Chapter 3 Review

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 4 Review

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

Chapter 5 Review

4 & 5 Cumulative Review Exercises

CHAPTER 6: TRIGONOMETRIC FUNCTIONS


PRECALCULUS

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 6 Review

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 7 Review

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

Chapter 8 Review

6, 7, & 8 Cumulative Review Exercises

CHAPTER 9: ADDITIONAL TOPICS IN ANALYTIC GEOMETRY

9-1 Conic Sections; Parabola

9-2 Ellipse

9-3 Hyperbola

9-4 Rotation of Axes

Chapter 9 Group Activity: Focal Chords

Chapter 9 Review

CHAPTER 10: SYSTEMS OF EQUATIONS AND INEQUALITIES;

MATRICES

10-1 Systems of Linear Equations

10-2 Solving Linear Systems Using Gauss-Jordan Elimination

10-3 Matrix Operations

10-4 Solving Linear Systems Using Inverse Matrices

10-5 Determinants and Cramer’s Rule

Chapter 10 Group Activity: Modeling with Systems of Linear Equations

10-6 Systems of Nonlinear Equations

10-7 Systems of Linear Inequalities

10-8 Linear Programming

Chapter 10 Review

CHAPTER 11: SEQUENCES AND SERIES

11-1 Sequences and Series

11-2 Mathematical Induction

11-3 Arithmetic and Geometric Sequences

11-4 Counting Techniques: Multiplication Principle, Permutations,

and Combinations

11-5 Sample Spaces and Probability

11-6 Binomial Formula

Chapter 11 Group Activity: Sequences Specified by Recursion Formulas

Chapter 11 Review

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

Chapter 12 Review

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

NEW


International Edition

ALGEBRA & TRIGONOMETRY

Second Edition



2010 (February 2009) \ Hardcover

ISBN: 9780077276515

ISBN: 9780070173002 [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 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.


Interior Design - The trim size of the book has been increased

to provide more white space on the page, improve readability, and

decrease the length of the book. The font size has been increased

throughout. The size of graphs and diagrams has been increased

where necessary.

Updated Examples - Titles have been added to Examples and

the Examples have been scrutinized for clarity, length, and relevance

to current topics. “Overlapping” Examples have been removed.

Learning Objectives - These are clearly tied to sub-sections in the

text. Margin “checkpoints” throughout each section let students know

when a specific learning objective has been covered and reinforces

the use of correct mathematical terms.

Suggested Homework - A list of suggested homework assignments

has been added to each exercise section in the Annotated

Instructor’s Edition to provide instructors with guidelines for developing

core, standard, extended, and in-depth assignments.

Organizational Changes - Coverage of absolute value equations

and inequalities has been added to Chapter 1. Chapters 2, 3, and

4 have been significantly reorganized based on reviewer feedback.


PRECALCULUS

Coverage of circles is now introduced in Chapter 2 with coverage of

the mid-point and distance formulas. Variation is now covered after

polynomial and rational functions. Coverage of one-to-one and inverse

functions has moved to Chapter 4 on Exponents and Logarithms.

Systems and Matrices are now covered in two separate chapters.


Chapter R: A Review of Basic Concepts and Skills

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

1-4 Complex Numbers

1-5 Solving Quadratic Equations

1-6 Solving Other Types of Equations

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

Chapter 3: Polynomial and Rational 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

3-6 Additional Insights into Rational Functions

3-7 Polynomial and Rational Inequalities

3-8 Variation: Function Models in Action

Chapter 4: Exponential and Logarithmic Functions

4-1 One-to-One and Inverse Functions

4-2 Exponential 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

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

Chapter 7: Applications of Trigonometry

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

Chapter 8: Systems of Equations and Inequalities

8-1 Linear Systems in Two Variables with Applications

8-2 Linear Systems in Three Variables with Applications

8-3 Nonlinear Systems of Equations and Inequalities

8-4 Systems of Inequalities and Linear Programming

Chapter 9: Matrices and Matrix Applications

9-1 Solving Systems Using Matrices and Row Operations

9-2 The Algebra of Matrices

9-3 Solving Linear Systems Using Matrix Equations

9-4 Applications of Matrices and Determinants: Cramer’s Rule, Partial

Fractions, and More

Chapter 10: Analytical Geometry and Conic Sections

10-1 Introduction to Analytic Geometry

10-2 The Circle and the Ellipse

10-3 The Hyperbola

10-4 The Analytic Parabola

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

Chapter 11: Additional Topics in Algebra

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 Summary and Concept Review

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 Algebra and Trigonometry

INVITATION TO PUBLISH






Visit McGraw-Hill Education (Asia)

Website: www.mheducation.asia


PRECALCULUS

NEW

Precalculus


International Edition

PRECALCULUS

Seventh Edition


2011 (January 2010)

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.


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.


CHAPTER R: BASIC ALGEBRAIC OPERATIONS

R-1 Algebra and Real Numbers

R-2 Exponents and Radicals

R-3 Polynomials: Basic Operations and Factoring

R-4 Rational Expressions: Basic Operations

Chapter R Review

CHAPTER 1: EQUATIONS AND INEQUALITIES

1-1 Linear Equations and Applications

1-2 Linear Inequalities

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 1 Review

CHAPTER 2: GRAPHS

2-1 Rectangular Coordinates

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 2 Review

CHAPTER 3: FUNCTIONS

3-1 Functions

3-2 Graphing Functions

3-3 Transformations of Functions

3-3 Quadratic Functions

3-5 Combining Functions; Composition

3-6 Inverse Functions

Chapter 3 Group Activity: Mathematical Modeling - Choosing a Long-

Distance Calling Plan

Chapter 3 Review

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 4 Review

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

Chapter 5 Review


PRECALCULUS

4 & 5 Cumulative Review Exercises

CHAPTER 6: TRIGONOMETRIC FUNCTIONS

6-1 Angles and Their Measure

6-2 Trigonometric Functions: A Unit Circle Approach

6-3 Solving Right Triangles

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 6 Review

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 7 Review

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

Chapter 8 Review

6, 7, & 8 Cumulative Review Exercises

CHAPTER 9: ADDITIONAL TOPICS IN ANALYTIC GEOMETRY

9-1 Conic Sections; Parabola

9-2 Ellipse

9-3 Hyperbola

9-4 Rotation of Axes

Chapter 9 Group Activity: Focal Chords

Chapter 9 Review

CHAPTER 10: SYSTEMS OF EQUATIONS AND INEQUALITIES;

MATRICES

10-1 Systems of Linear Equations

10-2 Solving Linear Systems Using Gauss-Jordan Elimination

10-3 Matrix Operations

10-4 Solving Linear Systems Using Inverse Matrices

10-5 Determinants and Cramer’s Rule

Chapter 10 Group Activity: Modeling with Systems of Linear Equations

10-6 Systems of Nonlinear Equations

10-7 Systems of Linear Inequalities

10-8 Linear Programming

Chapter 10 Review

CHAPTER 11: SEQUENCES AND SERIES

11-1 Sequences and Series

11-2 Mathematical Induction

11-3 Arithmetic and Geometric Sequences

11-4 Counting Techniques: Multiplication Principle, Permutations,

and Combinations

11-5 Sample Spaces and Probability

11-6 Binomial Formula

Chapter 11 Group Activity: Sequences Specified by Recursion Formulas

Chapter 11 Review

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

Chapter 12 Review

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

NEW


International Edition

PRECALCULUS

Second Edition



2010 (February 2009) \ Hardcover

ISBN: 9780077276508

ISBN: 9780070172982 [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 Precalculus

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, Precalculus 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.


Interior Design - The trim size of the book has been increased

to provide more white space on the page, improve readability, and

decrease the length of the book. The font size has been increased

throughout. The size of graphs and diagrams has been increased

where necessary.

Updated Examples - Titles have been added to Examples and

the Examples have been scrutinized for clarity, length, and relevance

to current topics. “Overlapping” Examples have been removed.

Learning Objectives - These are clearly tied to sub-sections in the

text. Margin “checkpoints” throughout each section let students know

when a specific learning objective has been covered and reinforces

the use of correct mathematical terms.

Suggested Homework - A list of suggested homework assignments

has been added to each exercise section in the Annotated

Instructor’s Edition to provide instructors with guidelines for developing

core, standard, extended, and in-depth assignments.

Organizational Changes - Coverage of absolute value equations

and inequalities has been added to Chapter 1. Chapters 2, 3, and


PRECALCULUS

4 have been significantly reorganized based on reviewer feedback.

Coverage of circles is now introduced in Chapter 2 with coverage of

the mid-point and distance formulas. Variation is now covered after

polynomial and rational functions. Coverage of one-to-one and inverse

functions has moved to Chapter 4 on Exponents and Logarithms.

Systems and Matrices are now covered in two separate chapters.


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

1-4 Complex Numbers

1-5 Solving Quadratic Equations

1-6 Solving Other Types of Equations

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

Chapter 3: Polynomial and Rational 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

3-6 Additional Insights into Rational Functions

3-7 Polynomial and Rational Inequalities

3-8 Variation: Function Models in Action

Chapter 4: Exponential and Logarithmic Functions

4-1 One-to-One and Inverse Functions

4-2 Exponential 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

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

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

Chapter 7: Applications of Trigonometry

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

Chapter 8: Systems of Equations and Inequalities

8-1 Linear Systems in Two Variables with Applications

8-2 Linear Systems in Three Variables with Applications

8-3 Partial Fraction Decomposition

8-4 Systems of Inequalities and Linear Programming

8-5 Solving Systems Using Matrices and Row Operations

8-6 The Algebra of Matrices

8-7 Solving Linear Systems Using Matrix Equations

8-8 Applications of Matrices and Determinants: Cramer’s Rule, Geometry,

and More

Chapter 9: Analytical Geometry

9-1 Introduction to Analytic Geometry

9-2 The Circle and the Ellipse

9-3 The Hyperbola

9-4 The Analytic Parabola

9-5 Nonlinear Systems of Equations and Inequalities

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

Chapter 10: Additional Topics in Algebra

10-1 Sequences and Series

10-2 Arithmetic Sequences

10-3 Geometric Sequences

10-4 Mathematical Induction

10-5 Counting Techniques

10-6 Introduction to Probability

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

A-4 Deriving the Equation of a Conic

A-5 More on Matrices

A-6 Deriving the Equation of a Conic

PRECALCULUS: GRAPHS AND MODELS

Third Edition




2009 (February 2008)

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.


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


PRECALCULUS

1-5 Operations on Functions; Composition

1-6 Inverse Functions

Chapter 1 Review

Chapter 1 Group Activity: Mathematical Modeling–Choosing a Long

Distance Calling Plan

CHAPTER 2 MODELING WITH LINEAR AND QUADRATIC FUNC-

TIONS

2-1 Linear Functions

2-2 Linear Equations and Models

2-3 Quadratic Functions

2-4 Complex Numbers

2-5 Quadratic Equations and Models

2-6 Additional Equation Solving Techniques

2-7 Solving Inequalities

Chapter 2 Review

Chapter 2 Group Activity: Mathematical Modeling in Population

Studies

Cumulative Review Exercise for Chapters 1 and 2

CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS

3-1 Polynomial Functions And Models

3-2 Polynomial Division

3-3 Real Zeros and Polynomial Inequalities

3-4 Complex Zeros and Rational Zeros of Polynomials

3-5 Rational Functions and Inequalities

3-6 Variation and Modeling

Chapter 3 Review

Chapter 3 Group Activity: Interpolating Polynomials

CHAPTER 4 MODELING WITH EXPONENTIAL AND LOGARITHMIC

FUNCTIONS

4-1 Exponential Functions

4-2 Exponential Models

4-3 Logarithmic Functions

4-4 Logarithmic Models

4-5 Exponential and Logarithmic Equations

Chapter 4 Review

Cumulative Review Chapters 3 and 4

Chapter 4 Group Activity: Comparing Regression Models

Cumulative Review Exercise for Chapters 3 and 4

CHAPTER 5 TRIGONOMETRIC FUNCTIONS

5-1 Angles and Their Measure

5-2 Trigonometric Functions: A Unit Circle Approach

5-3 Solving Right Triangles

5-4 Properties of Trigonometric Functions

5-5 More General Trigonometric Functions and and Models

5-6 Inverse Trigonometric Functions

Chapter 5 Review

Chapter 5 Group Activity: A Predator-Prey Analysis Involving Mountain

Lions and Deer

CHAPTER 6 TRIGONOMETRIC IDENTITIES AND CONDITIONAL

EQUATIONS

6-1 Basic Identities and Their Use

6-2 Sum, Difference, and Cofunction Identities

6-3 Double-Angle and Half-Angle Identities

6-4 Product-Sum and Sum-Product Identities

6-5 Trigonometric Equations

Chapter 6 Review

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

7-1 Law of Sines

7-2 Law of Cosines

7-3 Vectors in the Plane

7-4 Polar Coordinates and Graphs

7-5 Complex Numbers and De Moivre’s Theorem

Chapter 7 Review

Chapter 7 Group Activity: Conic Sections and Planetary Orbits

Cumulative Review Exercise for Chapters 5, 6, and 7

CHAPTER 8 MODELING WITH SYSTEMS OF EQUATIONS AND

INEQUALITIES

8-1 Systems of Linear Equations in Two Variables

8-2 Systems of Linear Equations in Three Variables

8-3 Systems of Linear Inequalities

8-4 Linear Programming

Chapter 8 Review

Chapter 8 Group Activity: Modeling with Systems of Equations

CHAPTER 9 MATRICES AND DETERMINANTS

9-1 Matrix Solutions to Linear Systems

9-2 Matrix Operations

9-3 Inverse of a Square Matrix

9-4 Matrix Equations and Systems of Linear Equations

9-5 Determinants

9-6 Properties of Determinants

9-7 Determinants and Cramer’s Rule

Chapter 9 Review

Chapter 9 Group Activity: Using Matrices to Find Cost, Revenue,

and Profit

Cumulative Review Exercise for Chapters 8 and 9

CHAPTER 10 SEQUENCES, INDUCTION, PROBABILITY

10-1 Sequences and Series

10-2 Mathematical Induction

10-3 Arithmetic and Geometric Sequences

10-4 Multiplication Principle, Permutations, and Combinations

10-5 Sample Spaces and Probability

10-6 Binomial Formula

Chapter 10 Review

Chapter 10 Group Activity: Sequences Specified by Recursion

Formulas

CHAPTER 11 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY

11-1 Conic Sections; Parabola

11-2 Ellipse

11-3 Hyperbola

11-4 Systems of Nonlinear Equations

11-5 Rotation of Axes

Chapter 11 Review

Chapter 11 Group Activity: Focal Chords

Cumulative Review Exercise for Chapters 10 and 11

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

PRECALCULUS WITH LIMITS

Sixth Edition



2008 (March 2007) \ Hardcover

ISBN: 9780073365800


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.


Chapter R: Basic Algebraic Operations

R-1 Algebra and Real Numbers

R-2 Exponents

R-3 Radicals

R-4 Polynomials: Basic Operations

R-5 Polynomials: Factoring

R-6 Rational Expressions: Basic Operations

Chapter R Review

Chapter R Review Exercises

Chapter R Group Activity: Rational and Irrational Numbers

Chapter 1: Equations and Inequalities

1-1 Linear Equations and Applications

1-2 Linear Inequalities

1-3 Absolute Value in Equations and Inequalities

1-4 Complex Numbers

1-5 Quadratic Equations and Applications

1-6 Additional Equation-Solving Techniques

Chapter 1 Review

Chapter 1 Review Exercises

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 Review

Chapter 2 Review Exercises

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 Operations on Functions; Composition

3-6 Inverse Functions

Chapter 3 Review

Chapter 3 Review Exercises

Chapter 3 Group Activity: Mathematical Modeling: Choosing a Long-

Distance Calling Plan

Cumulative Review Exercises Chapters 1-3

Chapter 4: Polynomials 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 Review

Chapter 4 Review Exercises

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 Review

Chapter 5 Review Exercises

Chapter 5 Group Activity: Comparing Regression Models

Cumulative Review Exercises Chapters 4-5

Chapter 6: Trigonometric Functions

6-1 Angles and Their Measure

6-2 Trigonometric Functions: A Unit Circle Approach

6-3 Solving Right Triangles

6-4 Properties of Trigonometric Functions

6-5 More General Trigonometric Functions and Models

6-6 Inverse Trigonometric Functions

Chapter 6 Review

Chapter 6 Review Exercises

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 Review

Chapter 7 Review Exercises

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 Review

Chapter 8 Review Exercises

Chapter 8 Group Activity: Conic Sections and Planetary Orbits

Cumulative Review Exercises Chapters 6-8

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 9 Review

Chapter 9 Review Exercises

Chapter 9 Group Activity: Focal Chords

Chapter 10: Systems of Equations and Inequalities; Matrices

10-1 Systems of Linear Equations in Two Variables

10-2 Systems of Linear Equations in Three Variables

10-3 Systems of Linear Equations: Gauss-Jordan Elimination

10-4 Matrix Operations

10-5 Systems of Linear Equations: Matrix Inverse Methods

10-6 Systems of Nonlinear Equations

10-7 Systems of Linear Inequalities in Two Variables

10-8 Linear Programming

Chapter 10 Review

Chapter 10 Review Exercises

Chapter 10 Group Activity: Modeling With Systems of Linear Equations

Chapter 11: Sequences, Induction, and Probability

11-1 Sequences and Series

11-2 Mathematical Induction

11-3 Arithmetic and Geometric Sequences

11-4 Multiplication Principle, Permutations, and Combinations

11-5 Sample Spaces and Probability

11-6 Binomial Formula


PRECALCULUS

Chapter 11 Review

Chapter 11 Review Exercises

Chapter 11 Group Activity: Sequences Specified by Recursion

Formulas

Cumulative Review Exercises Chapters 9-11

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 Review

Chapter 12 Review Exercises

Chapter 12 Group Activity: Derivatives of Exponential and Log Functions

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

37. Loci; Parabolas

38. Ellipses and Hyperbolas

39. Rotation of Axes

40. Conic Sections

41. Sequences and Series

42. The Principle of Mathematical Induction

43. Special Sequences and Series

44. The Binomial Theorem

SCHAUM’S OUTLINE OF PRECALCULUS

Second Edition


2009 (July 2008) / 426 pages / Softcover

ISBN: 9780071508643


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 precalculus

courses.


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

22. Trigonometric Identities and Equations

23. Sum, Difference, Multiple, and Half-Angle Formulas

24. Inverse Trigonometric Functions

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








Visit McGraw-Hill Education

Website: www.mheducation.asia


PRECALCULUS


CALCULUS

Applied/Business Calculus .................................................................................65

Calculus and Analytic Geometry.........................................................................67

Multi-Variable Calculus .......................................................................................76

Professional References ....................................................................................79

Single Variable Calculus .....................................................................................72


NEW TITLES

CALCULUS

2010 Author ISBN-13 Page

Applied Calculus for Business, Economics, and the Social and Life Sciences, Hoffmann 9780077297886 65

Expanded Edition

Calculus for Business, Economics, and the Social and Life Sciences, 10e Hoffmann 9780077292737 66


CALCULUS

NEW

Applied /

Business Calculus


International Edition

APPLIED CALCULUS FOR

BUSINESS, ECONOMICS,

AND THE SOCIAL AND LIFE

SCIENCES

Expanded Edition




2010 (January 2009) \ Hardcover

ISBN: 9780077297886

ISBN: 9780071311816 [IE]


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!


Improved Exercise Sets! - Almost 300 new routine and application

exercises have been added to the already extensive problem

sets. A wealth of new applied problems have been added to help

demonstrate the practicality of the material. These new problems

come from many fields, but in particular more applications focused

on economics have been added.

Enhanced Topic Coverage - Every section in the text underwent

careful analysis and extensive review to ensure the most beneficial

and clear presentation. Additional steps and definition boxes were

added when necessary for greater clarity and precision, and discussions

and introductions were added or rewritten as needed to improve

presentation.

New Contemporary Design - The Tenth Edition design has been

improved with a rich, new color palette; updated writing and calculator

exercises; and Explore! boxes icons, and all figures have been revised

for a more contemporary and visual aesthetic. The goal of this new

design is to provide a more approachable and student-friendly text.

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

Chapter 4: Exponential and Logarithmic Functions

4.1 Exponential Functions: Continuous Compounding

4.2 Logarithmic Functions

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

Chapter 11: Trigonometric Functions

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


Chapter 1: Functions, Graphs, and Limits

1.1 Functions

1.2 The Graph of a Function

1.3 Linear Functions

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


CALCULUS

NEW


International Edition

CALCULUS FOR BUSINESS,

ECONOMICS, AND THE

SOCIAL AND LIFE SCIENCES

Tenth Edition




2010 (January 2009) / Hardcover

ISBN: 9780077292737

ISBN: 9780071288903 [IE]


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!


Improved Exercise Sets! - Almost 300 new routine and application

exercises have been added to the already extensive problem

sets. A wealth of new applied problems have been added to help

demonstrate the practicality of the material. These new problems

come from many fields, but in particular more applications focused

on economics have been added.

Enhanced Topic Coverage - Every section in the text underwent

careful analysis and extensive review to ensure the most beneficial

and clear presentation. Additional steps and definition boxes were

added when necessary for greater clarity and precision, and discussions

and introductions were added or rewritten as needed to improve

presentation.

New Contemporary Design - The Tenth Edition design has been

improved with a rich, new color palette; updated writing and calculator

exercises; and Explore! boxes icons, and all figures have been revised

for a more contemporary and visual aesthetic. The goal of this new

design is to provide a more approachable and student-friendly text.

Procedural Examples & Boxes - Each new topic is approached

with careful clarity by providing step-by-step problem-solving techniques.

These techniques are demonstrated in the numerous procedural

examples and in the frequent procedural summary boxes

highlighting the techniques demonstrated.


Chapter 1: Functions, Graphs, and Limits

1.1 Functions

1.2 The Graph of a Function

1.3 Linear Functions

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

2.4 The Chain Rule

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

3.4 Optimization; Elasticity of Demand

3.5 Additional Applied Optimization

Chapter 4: Exponential and Logarithmic Functions

4.1 Exponential Functions: Continuous Compounding

4.2 Logarithmic Functions

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 Introduction to Differential Equations

6.3 Improper Integrals; Continuous Probability

6.4 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

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

INVITATION TO PUBLISH






Visit McGraw-Hill Education (Asia)

Website: www.mheducation.asia


CALCULUS

Calculus and

Analytic Geometry

CALCULUS: LATE TRANSCENDENTAL

FUNCTIONS

Third Edition



2008 (January 2007)

ISBN: 9780073312705

ISBN: 9780071101998 [IE]

ISBN: 9780077295950 [with Mathzone access card]


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

elegance of math in the world around us.


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 / 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

2.5 The Chain Rule

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

Chapter 4: Integration

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

4.6 Integration by Substitution

4.7 Numerical Integration / Error bounds for 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 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

6.2 Inverse Functions

6.3 Exponentials

6.4 The Inverse Trigonometric Functions

6.5 The Calculus of the Inverse Trigonometric Functions

6.6 The Hyperbolic Function

Chapter 7: First-Order Differential Equations

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

7.8 Probability

Chapter 8: First-Order Differential Equations

8.1 modeling with Differential Equations / Growth and Decay Problems

/ Compound Interest

8.2 Separable Differential Equations / Logistic Growth

8.3 Direction Fields and Euler’s Method / Systems of First Order

Equations

Chapter 9: Infinite Series

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

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 / Components and Projections

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 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

Chapter 13: Functions of Several Variables and Partial Differentiation


CALCULUS

13.1 Functions of Several Variables

13.2 Limits and Continuity

13.3 Partial Derivatives

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

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 / Mass and Center of Mass

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 Differential Equations

16.4 Power Series Solutions of Differential Equations

Appendix A: Proofs of Selected Theorems

Appendix B: Answers to Odd-Numbered Exercises

International Edition

CALCULUS WITH MATHZONE

Early Transcendental Functions

Third Edition



2007 (February 2006) / Hardcover with access card

ISBN: 9780073309446

ISBN: 9780071108072 [IE with MathZone]

ISBN: 9780071107518 [IE without MathZone]



Chapter 0: Preliminaries

0.1 Polynomials and Rational Functions

0.2 Graphing Calculators and Computer Algebra Systems

0.3 Inverse 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.

Chapter 1: Limits and Continuity

1.1 A First Look at Calculus

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. 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.

Chapter 2: Differentiation

2.1 Tangent Lines and Velocity

2.2 The Derivative Numerical Differentiation

2.3 Computation of Derivatives: The Power Rule. Higher Order

Derivatives. Acceleration.

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Derivatives of the Trigonometric Functions

2.7 Derivatives of the Exponential and Logarithmic Functions

2.8 Implicit Differentiation and Inverse Trigonometric Functions

2.9 The Mean Value Theorem.

Chapter 3: Applications of Differentiation

3.1 Linear Approximations and Newton’s Method

3.2 Indeterminate Forms and L’Hopital’s Rule

3.3 Maximum and Minimum Values

3.4 Increasing and Decreasing Functions

3.5 Concavity and the Second Derivative Test

3.6 Overview of Curve Sketching

3.7 Optimization

3.8 Related Rates

3.9 Rates of Change in Economics and the Sciences.

Chapter 4: Integration

4.1 Antiderivatives

4.2 Sums and Sigma Notation. Principle of Mathematical Induction

4.3 Area

4.4 The Definite Integral. Average Value of a Function

4.5 The Fundamental Theorem of Calculus

4.6 Integration by Substitution

4.7 Numerical Integration. Error Bounds for Numerical Integration

4.8 The Natural Logarithm as an Integral. The Exponential Function

as the Inverse of the Natural Logarithm.

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 Economics and the Sciences

5.7 Probability

Chapter 6: Integration Techniques

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

7.3 Direction Fields and Euler’s Method

7.4 Systems of First Order Differential Equations. Predator-Prey

Systems

Chapter 8: Infinite Series

8.1 Sequences of Real Numbers

8.2 Infinite Series

8.3 The Integral Test and Comparison Tests

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

8.6 Power Series

8.7 Taylor Series. Representations of Functions as Series. Proof

of Taylor’s Theorem.

8.8 Applications of Taylor Series. The Binomial Series.

8.9 Fourier Series.

Chapter 9: Parametric Equations and Polar Coordinates.

9.1 Plane Curves and Parametric Equations.


CALCULUS

9.2 Calculus and Parametric Equations.

9.3 Arc Length and Surface Area in Parametric Equations.

9.4 Polar Coordinates.

9.5 Calculus and Polar Coordinates.

9.6 Conic Sections.

9.7 Conic Sections in Polar Coordinates.

Chapter 10: Vectors and the Geometry of Space.

10.1 Vectors in the Plane.

10.2 Vectors in Space

10.3 The Dot Product. Components and Projections

10.4 The Cross Product

10.5 Lines and Planes in Space

10.6 Surfaces in Space.

Chapter 11: Vector-Valued Functions

11.1 Vector-Valued Functions

11.2 The Calculus of Vector-Valued Functions

11.3 Motion in Space

11.4 Curvature

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.

12.1 Functions of Several Variables

12.2 Limits and Continuity

12.3 Partial Derivatives

12.4 Tangent Planes and Linear Approximations. Increments and

Differentials.

12.5 The Chain Rule

12.6 The Gradient and Directional Derivatives

12.7 Extrema of Functions of Several Variables

12.8 Constrained Optimization and Lagrange Multipliers

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

13.7 Spherical Coordinates

13.8 Change of Variables in Multiple Integrals

Chapter 14: Vector Calculus

14.1 Vector Fields

14.2 Line Integrals

14.3 Independence of Path and Conservative Vector Fields

14.4 Green’s Theorem

14.5 Curl and Divergence

14.6 Surface Integrals

14.7 The Divergence Theorem

14.8 Stokes’ Theorem

14.9 Applications of Vector Calculus.

Chapter 15: Second Order Differential Equations

15.1 Second-Order Equations with Constant Coefficients

15.2 Nonhomogeneous Equations: Undetermined Coefficients

15.3 Applications of Second Order Equations

15.4 Power Series Solutions of Differential Equations.

Appendix A: Proofs of Selected Theorems

Appendix B: Answers to Odd-Numbered Exercises.

International Edition

CALCULUS: Concepts and Connections



2006 / 1,312 pages

ISBN: 9780073309293

ISBN: 9780073016078 (with MathZone)

ISBN: 9780071249027 [IE without MathZone]



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.

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.


CALCULUS

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

Second Edition


1996 / Hardcover / 880 pages

ISBN: 9780070576421


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

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

5-1 Introduction

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

6-1 Introduction

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

8-1 Introduction

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


CALCULUS

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

10-1 Introduction

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

14-1 Introduction

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

15-1 Introduction

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

21-6 Maxwell’s Equations : A Final Thought

Appendices

SCHAUM’S OUTLINE OF ADVANCED

CALCULUS

Third Edition


2010 (February 2010) /

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.


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


CALCULUS

Single Variable Calculus

International Edition

CALCULUS, SINGLE VARIABLE: LATE

TRANSCENDENTAL FUNCTIONS

Third Edition



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


248 Interactive Applets that help students master concepts and

procedures and functions, 1600 algorithms , and 113 e-Professors.


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 / 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

2.5 The Chain Rule

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

Chapter 4: Integration

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

4.6 Integration by Substitution

4.7 Numerical Integration / Error bounds for 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 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

6.2 Inverse Functions

6.3 Exponentials

6.4 The Inverse Trigonometric Functions

6.5 The Calculus of the Inverse Trigonometric Functions

6.6 The Hyperbolic Function

Chapter 7: First-Order Differential Equations

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

7.8 Probability

Chapter 8: First-Order Differential Equations

8.1 modeling with Differential Equations / Growth and Decay Problems

/ Compound Interest

8.2 Separable Differential Equations / Logistic Growth

8.3 Direction Fields and Euler’s Method / Systems of First Order

Equations

Chapter 9: Infinite Series

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

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 / Components and Projections


CALCULUS

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 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

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 / 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

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 / Mass and Center of Mass

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 Differential Equations

16.4 Power Series Solutions of Differential Equations

Appendix A: Proofs of Selected Theorems

Appendix B: Answers to Odd-Numbered Exercises

International Edition

CALCULUS: SINGLE VARIABLE

Early Transcendental Functions

Third Edition



2007 (December 2005) / Hardcover with access card

ISBN: 9780073309439

ISBN: 9780073215310 (with MathZone) - Out-of Print

ISBN: 9780071107860 [IE with MathZone]



Chapter 0: Preliminaries

0.1 Polynomials and Rational Functions

0.2 Graphing Calculators and Computer Algebra Systems

0.3 Inverse 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

Chapter 1: Limits and Continuity

1.1 A First Look at Calculus

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. 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.

Chapter 2: Differentiation

2.1 Tangent Lines and Velocity

2.2 The Derivative. Numerical Differentiation

2.3 Computation of Derivatives: The Power Rule. Higher Order

Derivatives. Acceleration.

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Derivatives of the Trigonometric Functions

2.7 Derivatives of the Exponential and Logarithmic Functions

2.8 Implicit Differentiation and Inverse Trigonometric Functions

2.9 The Mean Value Theorem

Chapter 3: Applications of Differentiation.

3.1 Linear Approximations and Newton’s Method

3.2 Indeterminate Forms and L’Hopital’s Rule

3.3 Maximum and Minimum Values

3.4 Increasing and Decreasing Functions

3.5 Concavity and the Second Derivative Test

3.6 Overview of Curve Sketching

3.7 Optimization

3.8 Related Rates

3.9 Rates of Change in Economics and the Sciences

Chapter 4: Integration

4.1 Antiderivatives

4.2 Sums and Sigma Notation. Principle of Mathematical Induction

4.3 Area

4.4 The Definite Integral. Average Value of a Function

4.5 The Fundamental Theorem of Calculus

4.6 Integration by Substitution

4.7 Numerical Integration. Error Bounds for Numerical Integration

4.8 The Natural Logarithm as an Integral. The Exponential Function

as the Inverse of the Natural Logarithm.

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 Economics and the Sciences


CALCULUS

5.7 Probability.

Chapter 6: Integration Techniques

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.

7.3 Direction Fields and Euler’s Method

7.4 Systems of First Order Differential Equations. Predator-Prey

Systems.

Chapter 8: Infinite Series

8.1 Sequences of Real Numbers

8.2 Infinite Series

8.3 The Integral Test and Comparison Tests

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

8.6 Power Series

8.7 Taylor Series. Representations of Functions as Series. Proof of

Taylor’s Theorem

8.8 Applications of Taylor Series. The Binomial Series

8.9 Fourier Series

Chapter 9: Parametric Equations and Polar Coordinates

9.1 Plane Curves and Parametric Equations

9.2 Calculus and Parametric Equations

9.3 Arc Length and Surface Area in Parametric Equations

9.4 Polar Coordinates

9.5 Calculus and Polar Coordinates

9.6 Conic Sections

9.7 Conic Sections in Polar Coordinates

Chapter 10: Vectors and the Geometry of Space

10.1 Vectors in the Plane

10.2 Vectors in Space

10.3 The Dot Product. Components and Projections

10.4 The Cross Product

10.5 Lines and Planes in Space

10.6 Surfaces in Space.

Chapter 11: Vector-Valued Functions

11.1 Vector-Valued Functions

11.2 The Calculus of Vector-Valued Functions

11.3 Motion in Space

11.4 Curvature

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.

12.1 Functions of Several Variables

12.2 Limits and Continuity.

12.3 Partial Derivatives

12.4 Tangent Planes and Linear Approximations. Increments and

Differentials.

12.5 The Chain Rule

12.6 The Gradient and Directional Derivatives

12.7 Extrema of Functions of Several Variables

12.8 Constrained Optimization and Lagrange Multipliers.

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

13.7 Spherical Coordinates

13.8 Change of Variables in Multiple Integrals

Chapter 14: Vector Calculus

14.1 Vector Fields

14.2 Line Integrals

14.3 Independence of Path and Conservative Vector Fields

14.4 Green’s Theorem

14.5 Curl and Divergence

14.6 Surface Integrals

14.7 The Divergence Theorem

14.8 Stokes’ Theorem

14.9 Applications of Vector Calculus

Chapter 15: Second Order Differential Equations

15.1 Second-Order Equations with Constant Coefficients

15.2 Non-homogeneous Equations: Undetermined Coefficients

15.3 Applications of Second Order Equations

15.4 Power Series Solutions of Differential Equations

Appendix A: Proofs of Selected Theorems

Appendix B: Answers to Odd-Numbered Exercises.

SCHAUM’S OUTLINE OF CALCULUS

Fifth Edition


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.


1. Linear Coordinate Systems. Absolute Value. Inequalities.

2. Rectangular Coordinate Systems

3. Lines

4. Circles

5. Equations and their Graphs

6. Functions

7. Limits

8. Continuity

9. The Derivative

10. Rules for Differentiating Functions

11. Implicit Differentiation

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

18. Inverse Trigonometric Functions

19. Rectilinear and Circular Motion

20. Related Rates

21. Differentials. Newton’s Method

22. Antiderivatives

23. The Definite Integral. Area under a Curve

24. The Fundamental Theorem of Calculus

25. The Natural Logarithm

26. Exponential and Logarithmic Functions

27. L’Hopital’s Rule

28. Exponential Growth and Decay

29. Applications of Integration I: Area and Arc Length

30. Applications of Integration II: Volume

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. Miscellaneous Substitutions

35. Improper Integrals

36. Applications of Integration II: Area of a Surface of Revolution

37. Parametric Representation of Curves

38. Curvature


CALCULUS

SCHAUM’S OUTLINE OF MATHEMATICA

Second Edition


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.


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

9. Integral Calculus

10. Multivariate Calculus

11. Ordinary Differential Equations

12. Linear Algebra

SCHAUM’S 3,000 SOLVED PROBLEMS IN

CALCULUS


2009 (September 2009) / 442 pages

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!

SCHAUM’S OUTLINE OF BEGINNING

CALCULUS

Third 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 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

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 EASY OUTLINES: CALCULUS


2000 / 135 pages

ISBN: 9780070527102





Chapter 1: Functions, Sequences, Limits, and Continuity.

Chapter 2: Differentiation.

Chapter 3: Maxima and Minima.

Chapter 4: Differentiation of Special Functions.

Chapter 5: The Law of the Mean, Indeterminate Forms, Differentials,

and Curve Sketching.

Chapter 6: Fundamental Integration Techniques and Applications.

Chapter 7: The Definite Integral, Plane Areas by Integration, Improper

Integrals.

Appendix A: Differentiation Formulas for Common Mathematical

Functions.

Appendix B: Integration Formulas for Common Mathematical Functions.

Index.


CALCULUS

SCHAUM’S OUTLINE OF UNDERSTANDING

CALCULUS CONCEPTS


1996 / 224 pages

ISBN: 9780070487383



What It’s All About.

The Derivative.

Applications of the Derivative.

The Integral.

Applications of the Integral.

Topics in Integration.

Infinite Series.

International Edition

SCHAUM’S OUTLINE OF DIFFERENTIAL

AND INTEGRAL CALCULUS, SI METRIC

Third Edition


1992

ISBN: 9780071125314 [IE]



Multi-Variable Calculus

CALCULUS: MULTIVARIABLE

Late Transcendental Functions

Third 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.


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 / 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

2.5 The Chain Rule

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


CALCULUS

3.4 Concavity and the Second Derivative Test

3.5 Overview of Curve Sketching

3.6Optimization

3.8 Related Rates

3.8 Rates of Change in Economics and the Sciences

Chapter 4: Integration

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

4.6 Integration by Substitution

4.7 Numerical Integration / Error bounds for 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 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

6.2 Inverse Functions

6.3 Exponentials

6.4 The Inverse Trigonometric Functions

6.5 The Calculus of the Inverse Trigonometric Functions

6.6 The Hyperbolic Function

Chapter 7: First-Order Differential Equations

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

7.8 Probability

Chapter 8: First-Order Differential Equations

8.1 modeling with Differential Equations / Growth and Decay Problems

/ Compound Interest

8.2 Separable Differential Equations / Logistic Growth

8.3 Direction Fields and Euler’s Method / Systems of First Order

Equations

Chapter 9: Infinite Series

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

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 / Components and Projections

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 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

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 / 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

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 / Mass and Center of Mass

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 Differential Equations

16.4 Power Series Solutions of Differential Equations

Appendix A: Proofs of Selected Theorems

Appendix B: Answers to Odd-Numbered Exercises


CALCULUS

International Edition

CALCULUS: MULTIVARIABLE:

EARLY TRANSCENDENTAL FUNCTIONS

Third Edition



2007 (February 2006) / Hardcover

ISBN: 9780073309378

ISBN: 9780073215327 (with MathZone) - Out-of-Print

ISBN: 9780071107877 [IE with MathZone]



Chapter 0: Preliminaries

0.1 Polynomials and Rational Functions

0.2 Graphing Calculators and Computer Algebra Systems

0.3 Inverse 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.

Chapter 1: Limits and Continuity

1.1 A First Look at Calculus

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. 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.

Chapter 2: Differentiation

2.1 Tangent Lines and Velocity.

2.2 The Derivative. Numerical Differentiation.

2.3 Computation of Derivatives: The Power Rule. Higher Order

Derivatives Acceleration

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Derivatives of the Trigonometric Functions

2.7 Derivatives of the Exponential and Logarithmic Functions

2.8 Implicit Differentiation and Inverse Trigonometric Functions

2.9 The Mean Value Theorem

Chapter 3: Applications of Differentiation

3.1 Linear Approximations and Newton’s Method

3.2 Indeterminate Forms and L’Hopital’s Rule

3.3 Maximum and Minimum Values

3.4 Increasing and Decreasing Functions

3.5 Concavity and the Second Derivative Test

3.6 Overview of Curve Sketching

3.7 Optimization

3.8 Related Rates

3.9 Rates of Change in Economics and the Sciences.

Chapter 4: Integration

4.1 Antiderivatives

4.2 Sums and Sigma Notation. Principle of Mathematical Induction.

4.3 Area

4.4 The Definite Integral. Average Value of a Function

4.5 The Fundamental Theorem of Calculus

4.6 Integration by Substitution

4.7 Numerical Integration. Error Bounds for Numerical Integration.

4.8 The Natural Logarithm as an Integral. The Exponential Function

as the Inverse of the Natural Logarithm.

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 Economics and the Sciences.

5.7 Probability

Chapter 6: Integration Techniques

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.

7.3 Direction Fields and Euler’s Method

7.4 Systems of First Order Differential Equations. Predator-Prey

Systems

Chapter 8: Infinite Series

8.1 Sequences of Real Numbers

8.2 Infinite Series

8.3 The Integral Test and Comparison Tests

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

8.6 Power Series

8.7 Taylor Series. Representations of Functions as Series. Proof of

Taylor’s Theorem

8.8 Applications of Taylor Series. The Binomial Series

8.9 Fourier Series.

Chapter 9: Parametric Equations and Polar Coordinates

9.1 Plane Curves and Parametric Equations

9.2 Calculus and Parametric Equations

9.3 Arc Length and Surface Area in Parametric Equations

9.4 Polar Coordinates

9.5 Calculus and Polar Coordinates

9.6 Conic Sections

9.7 Conic Sections in Polar Coordinates.

Chapter 10: Vectors and the Geometry of Space

10.1 Vectors in the Plane

10.2 Vectors in Space

10.3 The Dot Product. Components and Projections.

10.4 The Cross Product

10.5 Lines and Planes in Space

10.6 Surfaces in Space

Chapter 11: Vector-Valued Functions

11.1 Vector-Valued Functions

11.2 The Calculus of Vector-Valued Functions

11.3 Motion in Space

11.4 Curvature

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

12.1 Functions of Several Variables

12.2 Limits and Continuity

12.3 Partial Derivatives

12.4 Tangent Planes and Linear Approximations. Increments and

Differentials

12.5 The Chain Rule

12.6 The Gradient and Directional Derivatives

12.7 Extrema of Functions of Several Variables

12.8 Constrained Optimization and Lagrange Multipliers

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.

13.7 Spherical Coordinates

13.8 Change of Variables in Multiple Integrals.


CALCULUS

Chapter 14: Vector Calculus

14.1 Vector Fields

14.2 Line Integrals

14.3 Independence of Path and Conservative Vector Fields

14.4 Green’s Theorem

14.5 Curl and Divergence

14.6 Surface Integrals

14.7 The Divergence Theorem

14.8 Stokes’ Theorem

14.9 Applications of Vector Calculus.

Chapter 15: Second Order Differential Equations

15.1 Second-Order Equations with Constant Coefficients

15.2 Nonhomogeneous Equations: Undetermined Coefficients

15.3 Applications of Second Order Equations

15.4 Power Series Solutions of Differential Equations.

Appendix A: Proofs of Selected Theorems

Appendix B: Answers to Odd-Numbered Exercises

Professional References

FIVE STEPS TO A 5 AP CALCULUS AB AND

BC

Third Edition


2009 (November 2009) / Softcover

ISBN: 9780071624756


The effective, five-step plan to help you succeed on the AP Calculus

exam

The AP AB/BC Calculus exams have the largest enrollment of any

AP exam. This fully revised edition covers the latest course syllabus

of both subjects and provides model tests that reflect the latest versions

of the exams.

International Edition

HOW TO SOLVE WORD PROBLEMS IN

CALCULUS


2001 / 226 pages

ISBN: 9780071358972

ISBN: 9780071203838 [IE]



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.








Visit McGraw-Hill Education

Website: www.mheducation.asia


CALCULUS


HIGHER

MATHEMATICS

Advanced Engineering Mathematics ..................................................................92

Advanced Geometry ...........................................................................................99

Combinatorics.....................................................................................................90

Complex Analysis .............................................................................................100

Differential Equations .........................................................................................83

Differential Equations with Boundary Value Problems .......................................85

Functional Analysis ...........................................................................................103

Graph Theory .....................................................................................................93

History of Mathematics .......................................................................................95

Introductory Analysis ..........................................................................................94

Linear Algebra ....................................................................................................88

Number Theory ...................................................................................................98

Numerical Analysis .............................................................................................96

Partial Differential Equations ..............................................................................86

Professional References ..................................................................................105

Real Analysis ....................................................................................................104

Transition to Higher Math/Foundations of Higher Math ......................................87


NEW TITLES

HIGHER MATHEMATICS

2011 Author ISBN-13 Page

Elementary Number Theory, 7e Burton 9780077349905 98

The History of Mathematics: An Introduction, 7e Burton 9780073383156 95

HIGHER MATHEMATICS

2010 Author ISBN-13 Page

Numerical Methods for Engineers, 6e Chapra 9780073401065 96


HIGHER MATHEMATICS

Differential Equations

International Edition

DIFFERENTIAL EQUATIONS

Theory, Technique, and Practice



2007 (December 2005) / 768 pages / Hardcover

ISBN: 9780072863154 (Out-of-Print)

ISBN: 9780071254373 [IE]



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.

9.1 Introductory Remarks.

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

10.1 Introductory Remarks.

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

for Review and Discovery.

12 Dynamical Systems

12.1 Flows

12.1.1 Dynamical Systems


HIGHER MATHEMATICS

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

DIFFERENTIAL EQUATIONS


2005 (October 2005)

ISBN: 9780071250856


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

-

fully

chosen to 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


useful in helping them through the course.


Preface

1. Basic Concepts

2. Analytic Solutions

3. Graphical Techniques

4. Numerical Methods

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

International Edition

DIFFERENTIAL EQUATIONS

A Modeling Approach


2005 / 768 pages

ISBN: 9780072422290 (Out-of-Print)

ISBN: 9780071111515 [IE]



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 Per-


HIGHER MATHEMATICS

cussion.

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)

International Edition

DIFFERENTIAL EQUATIONS WITH

APPLICATIONS AND HISTORICAL NOTES

Second Edition


1991 / 640 pages

ISBN: 9780070575400 (Out-of-Print)

ISBN: 9780071128070 [IE]


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.

7 Partial Differential Equations and Boundary Value Problems.

8 Some Special Functions of Mathematical Physics.

9 Laplace Transforms.

10 Systems of First Order Equations.

11 Nonlinear Equations.

12 The Calculus of Variations.

13 The Existence and Uniqueness of Solutions.

14 Numerical Methods.

SCHAUM’S OUTLINE OF DIFFERENTIAL

EQUATIONS

Third Edition



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

with Boundary

Value Problems

International Edition

DIFFERENTIAL EQUATIONS

Theory, Technique, and Practice



2007 (December 2005) / 768 pages / Hardcover

ISBN: 9780072863154 (Out-of-Print)

ISBN: 9780071254373 [IE]



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


HIGHER MATHEMATICS

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.

9.1 Introductory Remarks.

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

10.1 Introductory Remarks.

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

for Review and Discovery.

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

Partial Differential

Equations

International Edition

FOURIER SERIES AND BOUNDARY VALUE

PROBLEMS

Seventh Edition



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.


Preface

1 Fourier Series

2 Convergence of Fourier Series

3 Partial Differential Equations of Physics

4 The Fourier Method

5 Boundary Value Problems

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


HIGHER MATHEMATICS

SCHAUM’S OUTLINE OF PARTIAL

DIFFERENTIAL EQUATIONS



1986 / 256 pages

ISBN: 9780070178977



Introduction.

Classification and Characteristics.

Qualitative Behavior of Solutions to Elliptic Equations.

Qualitative Behavior of Solutions to Evolution Equations.

First-Order Equations Eigenfunction Expansions and Integral Transforms:

Theory.

Eigenfunction Expansions and Integral Transforms: Applications.

Green’s Functions.

Difference Methods for Parabolic Equations.

Difference and Characteristic Methods for Parabolic Equations.

Difference Methods for Hyperbolic Equations.

Difference Methods for Elliptic Equations.

Variational Formulation of Boundary Value Problems.

The Finite Element Method: An Introduction.

Answers to Supplementary Problems.

Transition to Higher Math

/Foundations of Higher

Math

International Edition

TRANSITION TO HIGHER MATHEMATICS

Structure and Proof



2007 (February 2006) / 416 pages / Hardcover

ISBN: 9780073533537

ISBN: 9780071106474 [IE]


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

1.8. Exercises

Chapter 2. Relations

2.1. Definitions

2.2. Orderings

2.3. Equivalence Relations

2.4. Constructing Bijections

2.5. Modular Arithmetic

2.6. Exercises

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

4.5. Exercises

Chapter 5. Limits

5.1. Limits

5.2. Continuity

5.3. Sequences of Functions

5.4. Exercises

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

7.6. Exercises

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. Exercises

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

9.7. Exercises

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


HIGHER MATHEMATICS

Linear Algebra

International Edition

INTRODUCTION TO LINEAR ALGEBRA



2009 / Hardcover / 416 pages

ISBN: 9780073532356

ISBN: 9780071270540 [IE]


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.


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

Exercise Set 1.2

--1.3 Matrix Algebra

Exercise Set 1.3

--1.4 The Inverse of a Square Matrix

Exercise Set 1.4

--1.5 Matrix Equations

Exercise Set 1.5

--1.6 Determinants

Exercise Set 1.6

--1.7 Elementary Matrices and LU Factorization

Exercise Set 1.7

--1.8 Applications of Systems of Linear Equatio

Exercise Set 1.8

Review Exercises

Chapter Test

Chapter 2 Linear Combinations and Linear Independence

--2.1 Vectors in Rn

Exercise Set 2.1

--2.2 Linear Combinations

Exercise Set 2.2

--2.3 Linear Independence

Exercise Set 2.3

Review Exercises

Chapter Test

Chapter 3 Vector Spaces

--3.1 Definition of a Vector Space

Exercise Set 3.1

--3.2 Subspaces

Exercise Set 3.2

--3.3 Basis and Dimension

Exercise Set 3.3

--3.4 Coordinates and Change of Basis

Exercise Set 3.4

--3.5 Application : Differential Equations

Exercise Set 3.5

Review Exercises

Chapter Test

Chapter 4 Linear Transformations

--4.1 Linear Transformations

Exercise Set 4.1

--4.2 The Null Space and Range

Exercise Set 4.2

--4.3 Isomorphisms

Exercise Set 4.3

--4.4 Matrix Representation of a Linear Transformation

Exercise Set 4.4

--4.5 Similarity

Exercise Set 4.5

--4.6 Application : Computer Graphics

Exercise Set 4.6

Review Exercises

Chapter Test

Chapter 5 Eigenvalues and Eigenvectors

--5.1 Eigenvalues and Eigenvectors

Exercise Set 5.1

--5.2 Diagonalization

Exercise Set 5.2

--5.3 Application : Systems of Linear Different

Exercise Set 5.3

--5.4 Application : Markov Chains

Exercise Set 5.4

Review Exercises

Chapter Test

Chapter 6 Inner Product Spaces

--6.1 The Dot Product on Rn

Exercise Set 6.1

--6.2 Inner Product Spaces

Exercise Set 6.2

--6.3 Orthonormal Bases

Exercise Set 6.3

--6.4 Orthogonal Complements

Exercise Set 6.4

--6.5 Application : Least Squares Approximation

Exercise Set 6.5

--6.6 Diagonalization of Symmetric Matrices

Exercise Set 6.6

--6.7 Application : Quadratic Forms

Exercise Set 6.7

--6.8 Application : Singular Value Decomposition

Exercise Set 6.8

Review Exercises

Chapter Test

A Preliminaries

A.1 Algebra of Sets

Exercise Set A.1

A.2 Functions

Exercise Set A.2

A.3 Techniques of Proof

Exercise Set A.3

A.4 Mathematical Induction

Exercise Set A.4

Answers to Odd-Numbered Exercises


HIGHER MATHEMATICS

A.3 Techniques of Proof

Exercise Set A.3

A.4 Mathematical Induction

Exercise Set A.4

Answers to Odd-Numbered Exercises

LINEAR ALGEBRA WITH APPLICATIONS

Sixth Edition


2009 / Hardcover / 544 pages

ISBN: 9780070985100


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.


Chapter 1: Systems of Linear Equations

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

International Edition

ELEMENTARY LINEAR ALGEBRA

Second Edition


2004 / 608 pages / softcover

ISBN: 9780070911420

ISBN: 9780071234399 [IE]




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.

A.2 Induction.

A.3 Polynomials

SCHAUM’S OUTLINE OF LINEAR ALGEBRA

Fourth Edition



2009 (July 2008) / 480 pages

ISBN: 9780071543521


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

course scope and sequence. The ideal review for hundreds of

thousands of college and high school students who enroll in linear

algebra courses.


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


HIGHER MATHEMATICS

SCHAUM’S EASY OUTLINES: LINEAR

ALGEBRA



2003 \ Softcover

ISBN: 9780071398800


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 formatº 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.

SCHAUM’S 3,000 SOLVED PROBLEMS IN

LINEAR ALGEBRA


1989 / 496 pages

ISBN: 9780070380233



Vectors in R and C.

Matrix Algebra.

Systems of Linear Equations.

Square Matrices.

Determinants.

Algebraic Structures