## Mathematics 113

### Calculus I for Science and Engineering

Length of Course: 14 weeks

Classroom Hours per Week: 4 hours

Number of Credits: 3 credits

Prerequisite: B.C High School Pre Calculus 12 with a C or Math 100/110 with a B.

Corequisite: English 097

### Course Description

This is the first semester of a first year calculus program 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.

### Course Outline

Length Description

Week 1

Limits, Computing Limits, Limits at infinity, End Behavior of a Function

Week 2

Continuity, Continuity of Trigonometric, Exponential, and Inverse Functions

Week 3

The Derivative: Tangent lines and Rates of Change, The Derivative Function, Introduction to Techniques of Differentiation

Week 4

The Derivative: The Product and Quotient Rule,  Derivatives of Trigonometric Functions, The Chain Rule

Week 5

Implicit Differentiation,  Derivatives of Logarithmic Functions

Week 6

Derivatives of Exponential and Inverse Trigonometric Functions, Related Rates

Week 7

Linear Approximations and Differentials, L’Hopital’s Rule, Indeterminate Forms

Week 8

Analysis of Functions I: Increase, Decrease, and Concavity

Analysis of Functions II: Relative Extrema, Graphing Polynomials

Week 9

Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents

Curve Sketching

Week 10

Absolute Maxima and Minima

Applied Maximum and Minimum Problems

Week 11

Newton’s Method, Rolle’s Theorem, Mean-Value Theorem

Week 12

Antiderivatives

Week 13

Review

Week 14

Final Exam

### Textbooks

Calculus: Early Transcendentals, 10th edition by Anton, Bivens, and Davis.

### Course Evaluation

10-20% Quizzes and Homework Midterm Exams Final Exam

### Transferability

Please refer to the BC Transfer Guide www.bctransferguide.ca

### Instructors

Arman Ahmadieh B.Sc., M.Sc. (Sharif University of Technology)
Hayri Ardal, B.Sc.(Bogazici), Ph.D.(Simon Fraser)
Kim Peu Chew, B.Sc. (Nanjing), M.A., Ph.D. (British Columbia)