LENGTH OF COURSE: One Semester (14 weeks)

 

CLASSROOM HOURS PER WEEK: 4 hours of lectures

 

NUMBER OF UNITS OF CREDIT: 3 credit hours

PREREQUISITE: Math 12 with a "C", Columbia College Math 100 with a "C", or the equivalent.

 

AUDIENCE: This course is designed for serious students of mathematics, science, or engineering.

 

First year calculus for students in the sciences or engineering. The course covers continuity, derivatives and antiderivatives of the elementary functions, and applications of the derivative in graphing and extremum problems.

 

1) Limits and Continuity (3 weeks)

Definition of the limit of a function, limit theorems, one-sided limits, limits at infinity, trigonometric limits, continuity, intermediate value theorem.

 

2) Exponential and Logarithmic Functions (2 weeks)

Inverse functions, exponential and logarithmic functions, exponential growth and decay.

 

3) The Derivative (3 weeks)

Definition of the derivative, differentiability, derivative of a polynomial, product rule, quotient rule, chain rule, derivatives of trigonometric functions, derivatives of exponential and logarithmic functions, significance of the derivative.

 

4) Applications of the Derivative (4 weeks)

Extrema of a function, mean value theorem, increasing and decreasing functions, concavity, critical points, curve sketching, derivatives of inverse functions including logarithmic functions and inverse trigonometric functions, implicit differentiation, differentials, maximum-minimum problems, related rates, examples from physics.

 

5) Integration (1 week)

Definite integral. Area. The Fundamental Theorem of Calculus.

 

James Stewart, Calculus, Third Edition, Brooks/Cole, 1995.

Sections of the textbook relevant to the above topics:

1) Chapter 1 2) Chapter 6 3) Chapter 2 4) Chapter 3 5) Chapter 4

 

Quizzes and/or Assignments 10%

Three One-Hour Exams 40%

Comprehensive Final Exam 50%

 

Kim Peu Chew, B.Sc. (Nanyang), M.A., Ph.D. (British Columbia)

Sam Ekambaram, B.Sc. (Madras), Ph.D. (Simon Fraser)

Peter Hurthig, B.Sc., M.Sc. (British Columbia)

David Medalen, B.A. (St. Olaf), M.Sc. (British Columbia)