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Mathematics 213

Calculus III

Length of Course: 14 weeks

Classroom Hours per Week: 4 hours of lecture and 1 hour of tutorial 

Number of Credits: 3 

Prerequisite: Mathematics 114 and 12 credits.

Course Description

An introduction to calculus of several variables, treating limits and continuity, partial derivatives, extrema, the chain rule, double, triple and path integrals.

Course Outline

Length Description

Week 1

Parametric Equations; Tangent Lines and Arc Length for Parametric Curves, Polar Coordinates, Tangent Lines, Arc Length, Area for Polar Curves

Week 2

Conic Sections, Rotation of Axes, Conic Sections in Polar Coordinates

Week 3

Rectangular Coordinates in 3-Space, Spheres, Cylindrical Surfaces

Vectors, Dot Product, Projections

Week 4

Cross Product, Parametric Equations of Lines, Planes in 3-Space

Week 5

Quadric Surfaces, Cylindrical and Spherical Coordinates

Week 6

Functions of Two or More Variables

Limits and Continuity

Partial Derivatives

Week 7

Differentiability, Differentials, Local Linearity

The Chain Rule

Directional Derivative and Gradient

Week 8

Tangent Plane and Normal Vector

Maxima and Minima of Functions of Two Variables

Lagrange Multipliers

Week 9

Double Integral

Double Integrals over Nonrectangular Regions

Double Integrals in Polar Coordinates

Week 10

Surface Area: Parametric Surfaces

Triple Integrals

Triple Integrals in Cylindrical and Spherical Coordinates

Week 11

Change of Variables in Multiple Integrals; Jacobians

Vector Valued Functions

Week 12

Vector Fields, Line Integrals, Green’s Theorem

Week 13


Week 14

Final Exam


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

Course Evaluation

Quizzes and Homework 10-20%
Midterm Exam(s) 30-40%
Final Exam 50%

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)
Ana Culibrk, B.Sc.,M.Sc. (Belgrade),M.Sc.(British Columbia)
Rika Dong, B.Sc. (Simon Fraser), M.Sc. (Regina)
Sam Ekambaram, B.Sc., M.Sc. (Madras), M.Sc., Ph.D. (Simon Fraser)
Himadri Ganguli, B.Sc., M.Sc. (Chennai), Ph.D. (Simon Fraser)
Peter Hurthig, B.Sc., M.Sc. (British Columbia)

Transferability: see