MATH 324 C
Advanced Multivariable Calculus

University of Washington, Autumn 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 8th Edition of Calculus: Early Transcendentals by James Stewart.


Name: Lucas Braune
E-mail: lvhb 'at'
Office: Padelford Hall C-526
Office hours: Mondays and Thursdays from 4 to 5 p.m. and Wednesdays from 3:30 to 4:30 p.m.

Time and place

When: Monday, Wednesday and Friday, from 10:30 to 11:20 a.m.
Where: Condon Hall, Room 109

Calendar and lecture notes

Day Topics
Sep 26 §15.1-3: Double integrals (notes)
Sep 28 §15.3-4: Double integrals, polar coordinates (notes)
Oct 1 §15.3-4: Polar coordinates, applications (notes)
Oct 3 §15.4, §14.5: Applications, review of vectors (notes)
Oct 5 §15.5-6: Surface area, triple integrals (notes)
Oct 8 §15.6: Triple integrals (notes)
Oct 10 §15.6-7: Triple integrals, cylindrical coordinates (notes)
Oct 12 §15.8: Spherical coordinates (notes)
Oct 15 §15.9: Change of variables (notes, supplementary notes)
Oct 17 §15.1-9: Review (notes)
Oct 19 First Midterm
Oct 22 §14.5-6: Chain rule, gradient vector (notes)
Oct 24 §14.6, §16.1: Gradient vector, vector fields (notes)
Oct 26 §16.2: Line integrals (notes)
Oct 29 §16.2: Line integrals (notes)
Oct 31 §16.2-3: Line integrals, the fundamental theorem (notes)
Nov 2 §16.3: Gradient fields (notes, supplementary notes)
Nov 5 §16.3: Test for gradient fields, Green's theorem (notes)
Nov 7 §16.4: Green's theorem (notes)
Nov 9 §16.4-5: Green's theorem; divergence and curl (notes)
Nov 12 No class: Veterans day (observed)
Nov 14 §14.5-6: Review for Midterm 2 (notes)
Nov 16 Second Midterm
Nov 19 §16.5: Divergence and curl in 3D (notes)
Nov 21 §16.6: Parametrization of surfaces; tangent planes (notes)
Nov 23 No class: Thanksgiving Friday
Nov 26 §16.6-7: Surface area, surface integrals (notes, supplementary notes)
Nov 28 §16.7: Surface integrals and flux (notes)
Nov 30 §16.8: The divergence theorem (notes, supplementary notes)
Dec 3 §16.9: Stokes' theorem (notes, supplementary notes)
Dec 5 §15.1-9, §14.4-5, §16.1-10: Course review I (notes)
Dec 7 §15.1-9, §14.4-5, §16.1-10: Course review II
Dec 10 Final Exam


Homework will generally be due at 11:00 p.m. on Wednesdays. No extensions will be given to anyone for any reason. You may miss 10% of the total of homework points available for the quarter without penalty to your grade.

Homework will be assigned and collected via Webassign. This link contains instructions on how to purchase Webassign access along with an electronic copy of the course text. An access code will be required after a two-week grade period at the beginning of the quarter.

If you are having trouble with your access code, consider attending the "office hours" held by Webassign representatives on Thursday, September 27 and Monday, October 1 from 11 a.m. to 3 p.m. at the Math Study Center (Communications Building, room B-014).

Please use this link to log into WebAssign.


Our course will have two midterm exams and one final exam. They will take palce at CDH 109, the room where our class will meet for lectures. The midterm exams will be given on October 19 and November 16 during lecture (from 10:30 to 11:20 a.m.). The final exam will be given on December 10 from 08:30 to 10:20 am.

Students may bring to exams a TI 30X IIS calculator and note sheet. The note sheet must be letter-size and handwritten (both sides are OK). If you want to use a nongraphing calculator other than the TI 30X IIS, talk to me (the instructor) before the day of the exam so that I can approve your device. Note that exam problems will be designed so as not to require a calculator for their solution.

Make-up exams will not be given. If you miss an exam due to unavoidable, compelling, and well-documented circumstances, your final exam will be weighted more heavily. In case of observance of religious holidays or participation in university sponsored activities, please contact me at least one week in advance. You will be asked to provide documentation for your absence.

Exam grades will be published on Catalyst.


The course grade will consist of the following:

Homework (due Wednesdays) 10%
Midterm 1 (Oct 19) 25%
Midterm 2 (Nov 16) 25%
Final Exam (Dec 10) 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.