MATH 324 C
Advanced Multivariable Calculus

Spring 2018

Course description

Multivariable calculus is the mathematics of fields and continuos media. As such, it is the language of electromagnetism, Newtonian gravity, fluid mechanics and the theory of elasticity. In this course, you will learn about double and triple integrals; changes of variables; polar, cylindrical and spherical coordinate systems; line and surface integrals; vector fields; flux and divergence; and circulation and curl.

The course textbook is the 7th Edition of Calculus: Early Transcendentals by James Stewart.


Name: Lucas Braune
E-mail: lvhb 'at'
Office: Padelford C-526
Office hours: MW, from 4:30 to 6:00pm.

Time and place

When: Mondays, Wednesdays and Fridays, from 10:30 to 11:20am
Where: Smith Hall, Room 105

Calendar and lecture notes

Day Topics Notes
March 26 §15.1-3: Double integrals (PDF)
March 28 §15.3-4: Double integrals, polar coordinates (PDF)
March 30 §15.4-5: Polar coordinates, applications (PDF)
April 2 §15.4-5, §14.5: Polar coordinates, reivew of vectors (PDF)
April 4 §15.6-7: Surface area, triple integrals (PDF)
April 6 §15.7-8: Triple integrals, cylindrical coordinates (PDF)
April 9 §15.9, §14.5: Spherical coordinates, determinants (PDF)
April 11 §15.10: Change of variables in multiple integrals (PDF)
April 13 §15.2-10: Hyperbolic coordinates, review (PDF)
April 16 First Midterm
April 18 §14.5-6: Chain rule, the gradient vector (PDF)
April 20 §14.6, §16.1: Directional derivatives (PDF)
April 23 §16.1-2: Vector fields, line integrals (PDF)
April 25 §16.2: Line integrals (PDF)
April 27 §16.2-3: Work, the fundamental theorem (PDF)
April 30 §16.3: Conservative vector fields (PDF)
May 2 §16.2-3: Review
May 4 §16.4: Green's theorem (PDF)
May 7 §16.5: Curl and divergence, Green's theorem (PDF)
May 9 §14.4-5, §16.1-5: Review for Midterm 2 (PDF)
May 11 Second Midterm
May 14 §16.5-6: Div and curl in 3D, parametrization of surfaces (PDF)
May 16 §16.6-7: Integrals over parametrized surfaces (PDF)
May 18 §16.6-7: Integrals over implicit surfaces (PDF)
May 21 §16.7: Integrals of vector fields, flux (PDF)
May 23 §16.9: The divergence theorem (PDF)
May 25 §16.8: Stokes' theorem (PDF)
May 28 No class: Memorial day
May 30 §16.1-10: Review; Maxwell's equations (PDF)
June 1 §15.2-10, §14.4-5, §16.1-10: Course review (PDF)
June 4 Final Exam

Homework and exams

Homework for this course must be submitted through Webassign.

Exam grades will be published on Catalyst.

The course grade will consist of the following:

Homework 10%
Midterm 1 25%
Midterm 2 25%
Final Exam 40%

Supplementary materials

A good source of practice problems is the Math 324 Exam Archive compiled by Andrew Loveless.

Another good source are the problem sets and sample exams from the multivariable calculus course made available by MIT here. Our quarter-long course will cover the second half of MIT's (which lasted one semester), but in a slightly different order. Relevant to us are lectures 16 through 35, problem sets 7 through 12, and exams 3 and 4.

Supplementary notes (optional)
Conservative fields (PDF)
The heat equation (PDF)
Proof of Stokes' theorem (PDF)