Mathematics 114

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 152 (3)
    University of British Columbia - Mathematics 101 (1.5)
    University of Victoria - Mathematics 101 (1.5)
PREREQUISITE: Columbia College Mathematics 113 or the equivalent.
 
AUDIENCE: This course is designed for serious students of mathematics and/or science.
 
CALENDAR DESCRIPTION
A continuation of Mathematics 113 covering antiderivatives, techniques of integration, definite integrals, polar coordinates, sequences and series, and Taylor series.
COURSE OUTLINE
1) Methods of Integration (5 weeks)
Substitution, integration by parts, reduction formulas, trigonometric integrals, trigonometric substitution, partial fractions, trapezoidal rule, Simpson's rule, improper integrals.
 
2) Applications of Integration (3 weeks)
Volume by cross sections, volume of a solid of revolution, parametric curves, arc length, surface area, work.
 
3) Sequences and Series (4 weeks)
Basic definitions of sequences and series, comparison tests, integral test, absolute and conditional convergence, ratio and root tests, power series, Taylor series, Maclaurin series.
 
4) Polar Coordinates (1 week)
Polar coordinates, conics in polar coordinates, tangent line to a polar curve, area in polar coordinates, length of a polar curve.
 
TEXTBOOK: James Stewart, Calculus, Third Edition, Brooks/Cole Publishing Company, 1995
    Sections in the textbook relevant to the above topics: Chapters 5, 7, 8, 9, 10
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)