# MULTIVARIABLE and VECTOR CALCULUS

### Department of Mathematics,  University of British Columbia

Prerequisites: One of SCIE 001, PHYS 101, 107, 121, 153 and one of SCIE 101, PHYS 102, 108, 122, 153 and one of SCIE 001, MATH 101, MATH 103, MATH 105, MATH 121.

Corequisites: one of MATH 152, 221, 223.

## Instructor

### Joel Feldman

 E-mail feldman@math.ubc.ca Office Math 221 Phone 604-822-5660 Home page http://www.math.ubc.ca/~feldman/ Office hours Tues 9:00-10:00, Tues 15:00-16:00, Thr 15:00-16:00

## Class Times and Location

• The course meets Monday, Wednesday from 11:00 to 11:50 in room Chemistry 300 and Friday from 10:00 to 11:50 in room Scarfe 100.

## Text

• Robert A. Adams, Calculus of Several Variables, fifth edition, Pearson Education Canada. The ISBN number is 0201798026.

I will post all handouts, problem sets, etc. on the web here.

## Topics

1. Vectors and the Geometry of Space (§10.1-10.4):
Three dimensional coordinate systems,
Vectors, dot and cross products, projections
Equations of lines and planes.
2. Vector Functions (§11.1,11.3):
Vector functions and space curves, parametrization
Derivatives and integrals of vector functions,
Arc length, speed, velocity and acceleration. Exclude curvature, normal, binormal, torsion.
3. Partial Derivatives (§ 10.5, 12.1-12.9, 13.1-13.3, 13.6):
Functions of several variables: visualizaton, quadrics,
Limits, partial derivatives,
Tangent planes and linear approximations,
Local maxima and minima, Lagrange multipliers,
Newton's method.
4. Multiple Integrals (§14.1-14.6):
Double and iterated integrals, polar coordinates, changing the order of integration
Applications, surface area,
Triple integrals, changing the order of integration
Cylindrical and Spherical co-ordinates.
5. Vector Fields and Line Integrals (§15.1-15.4):
Vector fields, conservative fields, potentials, line integrals.
6. Surface integrals (§15.5, 15.6):
Surfaces, parametrization, flux integrals, surface area, applications.
7. Integral Theorems (§16.1-16.6):
Gradient, divergence and curl, vector identities, divergence theorem,
Green's theorem, Stokes' theorem, applications.