## COURSE OUTLINE

## MATH 253 Section 103, Term 1 of 2005-06

## MWF at 11 am in Math 104

Instructor: Denis Sjerve

Office: 107 Math Building. Office Hours: MW 1:00 to 2:30, or by appointment.

Office Phone: (604) 822-2714 Email: sjer@math.ubc.ca

Web page: www.math.ubc.ca/~sjer

Textbook:
J. Stewart, Multivariable Calculus, fifth edition, Brooks/Cole publishers.

Course description: This course explores techniques and applications of calculus, for functions involving
several variables. It is intended for students in the Faculty of Applied Science.

Outline of Topics:

(1) Coordinate systems and vectors (8 hours): Points and vectors in 3-dimensions, dot and cross products.
Polar, cylindrical and spherical coordinates. Equations of lines and planes. (Sections 11.3-11.4, 13.1-13.7)

(2) Partial derivatives and applications (12 hours). Functions of several variables. Partial derivatives, tangent planes, linear approximation, gradient vector. Chain rule. Higher order partial derivatives. Maximum
and minimum values, Lagrange multipliers. Applications. (Sections 15.1-15.8)

(3) Multiple integrals (12 hours): Double and triple integrals. Different coordinate systems. Applications. (Sections 16.1-16.9)

Homework, Exams, Grades:
Homework will be assigned on a weekly basis (check this web page) but NOT collected. Answers to the
homework assignments will also be posted. A short quiz
will be given every two weeks (approximately), which will be strongly based
on the homework assignments. No make-up quizzes will be permitted; however, the lowest grade among the quizzes (which will be zero if missed) will be ignored.
There will be one midterm exam (50 minutes) on Wednesday, October 26.
The final exam will be 2 1/2 hours, scheduled by the university during the December exam period.
Your course grade will be calculated as follows:

30% quizzes + 20% midterm + 50% final exam

The instructor reserves the right to revise or round off grades if circumstances warrant. No make-up exams will be given in any circumstances, except in hardship cases for the final exam (3 exams in a 24 hour period), according to Senate regulations. Calculators, cellphones, electronic devices, books or notes are not allowed in exams or quizzes.