Mathematics 213

Course Outline

LENGTH OF COURSE: One Semester (14 weeks)
 
CLASSROOM HOURS PER WEEK: 4 hours of lectures
 
NUMBER OF UNITS OF CREDIT: 3 credit hours
    Simon Fraser University - 3 credit hours
    University of British Columbia - 3 credit hours
    University of Victoria - 1.5 units
PRESENT TRANSFERABILITY
    Simon Fraser University - Mathematics 251 (3)
    University of British Columbia - Mathematics 200 (1.5)
    University of Victoria - Mathematics 200 (1.5)
PREREQUISITE: Columbia College Mathematics 113 and 114 or the equivalent.
 
AUDIENCE: This course is designed for serious students of mathematics and/or science.
 
CALENDAR DESCRIPTION
An introduction to calculus of several variables, treating limits and continuity, partial derivatives, extrema, the chain rule, path integrals and double and triple integrals.
 
COURSE OUTLINE
1) Vectors in 3-space (1 week)
Rectangular coordinates in space, vectors in space, scalar product, cross product, lines and planes in space, cylindrical and spherical coodinates.
 
2) Functions of Several Variables (3.5 weeks)
Real-valued functions, limits and continuity, differentiability, partial derivatives and their properties, chain rule, gradients and directional derivatives, tangent plane to a surface.
 
3) Vector-Valued Functions (2 weeks)
Space curves, parametric equations, arc length, tangent vector to space curves, velocity and acceleration, vector fields, divergence and curl of a vector field.
 
4) Extrema (2 weeks)
Taylor's theorem, extrema of real-valued functions, constrained extrema and Lagrange multipliers, implicit function theorem.
 
5) Multiple Integration (3.5 weeks)
Double and triple integrals and their evaluation, centre of mass, centroids, moments of inertia, changing the order of integration, double integrals in polar coordinates, triple integrals in cylindrical and spherical coordinates, change of variable.
 
6) Path Integrals (1 week)
Path and line integrals.
 
TEXTBOOK
    James Stewart, Calculus, Third Edition, Brooks/Cole, 1995
    Sections of the textbook relevant to the above topics: Chapters 11, 12, 13, 14
COURSE EVALUATION
    Quizzes and/or assignments 10%
    Three One-Hour Tests 40%
    Comprehensive Final Examination 50%
INSTRUCTORS
    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. (Briitsh Columbia)
    David Medalen, B.A. (St.Olaf), M.Sc. (British Columbia)