Math 201-103-RE Differential Calculus - SLC Home Page

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2004.doc
Math 201-103-RE
Differential Calculus
Ponderation: 3-2-3 Credits: 2 2 3
Fall 2004
Periods: 14-24-34-44-54
Johann Carl Friedrich
Gauss
Instructor: Steve Hardy Telephone: 656-6921 (ext. 272)
Office: Room 334 Email: shardy@slc.qc.ca
Prerequisite: Compulsory: Secondary V Mathematics (526 or 536)
Textbook: Larson & Edwards Calculus: An Applied Approach 6 th Ed. Houghton Mifflin Co., 2003
ISBN: 0-618-21869-6
Programme Objectives: In this course you will see some of the contributions of calculus to the understanding of the human
phenomena, partially satisfying objective 022N. The elements of this objective are:
1) To understand the development of differential calculus.
2) To know and understand the main facts, notions, concepts, theories, methods and other key
components of differential calculus.
3) To demonstrate the relevance and scope of these components in the understanding of the human
phenomena.
Course Objectives: In this course you will use the methods of differential calculus to study functional models in the field of
Social Science, satisfying objective 022X of the Social Science Programme. The elements of this objective
are:
1) To situate the historical context of the development of differential calculus.
2) To recognize and describe the characteristics of algebraic, exponential, logarithmic and
trigonometric functions expressed in symbolic or graphic form.
3) To analyze the behaviour of a function represented in symbolic or graphic form using an intuitive
approach to the concept of limits.
4) To define the derivative of a function, to interpret it and apply derivative techniques.
5) To analyze the variations of a function using differential calculus.
6) To solve optimization and rate of change problems.
Course Description: The course will follow the lecture method with frequent problem solving interludes during which the
teacher will be available for individual help.
Student should feel free and are welcome to ask questions at any point during the lecture.
Absences: Attendance is mandatory and a maximum of 7 absences will be tolerated (explained and/or unexplained).
More than the 7 absences may mean failure in the course.
Rules & Regulations: St. Lawrence Campus has definite regulations concerning cheating, plagiarism and the quality of written
English which are clearly indicated in the Student Handbook and the St. Lawrence Campus Prospectus.
Students may be given a “0” on any work that involves cheating and plagiarism. It will be assumed that all
students have read and understood these rules and regulations.

Evaluation:
The evaluation of this course will verify that you have learned the following:
1) To use the appropriate concepts.
2) To represent situations through the use of functions.
3) To sketch adequate graphic representations of functions.
4) To choose and apply the correct differentiation rules and techniques.
5) To manipulate algebraic expressions correctly.
6) To make accurate calculations.
7) To arrive at correct interpretations of results.
8) To justify the steps you have taken in problem solving.
9) To use the appropriate terminology (notation).
The final grade will be obtained through:
Gifts: Regular "Gifts" (i.e. homework) will be given. Students will be expected to submit their "Gift" the
following school day in a NEAT and LEGIBLE way at the beginning of class, LATE "Gifts" will not be
accepted.
Quizzes: Regular (weekly, ~10 minutes) quizzes will be given during the semester on the topic(s) covered during the
week. A student missing a quiz will automatically be given the result “0” for that quiz.
Tests: • There will be 3 class test during the semester which are compulsory. A student missing a test will
automatically be given the result “0” for that test.
• Students are responsible for knowing when a test will be given. Ignorance of a test date will not be
considered a valid excuse.
• In the event that the college closes or the teacher is absent on a scheduled Quiz/Test date, the Quiz or
Test is moved to the next school day automatically.
Final Exam: There will be a three hours comprehensive final examination at the end of the semester.
Grading
Scheme:
Course Content:
The final grades will be calculated as follows:
Final Grade
Gifts Approximately 40 . . . . . . . . . . . 10%
Quiz Approximately 10 . . . . . . . . . . . 10%
Test 3 @ 15% each . . . . . . . . . . . 45%
Final Exam . . . . . . . . . . . 35%
0. REVIEW:
a) Factoring, Functional Notation.
1. LIMITS:
a) Concept of a Limit.
b) Limits at Infinity.
c) Secant and Tangent Lines.
d) Properties of Limits and their Use.
e) Concept of Continuity.
2. DERIVATIVES AND DIFFERENTIATION:
a) Concept of a Derivative.
b) Properties of Derivatives.
c) Differentiation Rules and Formulas.
d) Rates of Changes & Related Rates.
e) The Chain Rule.
f) Implicit Differentiation.
g) Higher Order Derivatives.
h) Differentials.
i) The Mean Value and Rolle’s Theorem.
1 These topics will only be covered if time allows.
3. DERIVATIVES OF SPECIAL FUNCTIONS:
a) Derivative of Trigonometric Functions.
b) Derivative of Exponential Functions.
c) Derivative of Logarithmic Functions.
d) Derivative of Inverse Trig. Functions.
4. APPLICATIONS:
a) Related Rates
b) Linear Approximation using Differentials.
c) Newton-Raphson’s Method. 1
d) Exponential Growth and Decay.
e) Optimization
f) Curve Sketching.
g) Indeterminate Forms and L’Hôpital’s Rule.