MATH 324 G
Advanced Multivariable Calculus

University of Washington, Autumn 2019


Name: Lucas Braune
E-mail: lvhb 'at'
Office: Padelford Hall C-526
Office hours: Mondays and Thursdays, from 4:00 to 5:00 p.m.

Time and place

When: Mondays, Wednesday and Fridays from 11:30 a.m. to 12:20 p.m.
Where: Smith Hall, Room 105 (SMI 105)


The course syllabus is here.

Lecture Notes

§15.1-2: Double integrals (pdf)
§15.3-4: Polar coordinates and applications (pdf)
§12.3-4: Dot products, cross products, and determinants (pdf)
§15.5: The area of a graph (pdf)
§15.6: Triple integrals (pdf)
§15.7: Cylindrical coordinates (pdf)
§15.8: Spherical coordinates (pdf)
§15.9: Change of coordinates (pdf)
§14.5-6: Chain rule, gradient vector and directional derivatives (pdf)
§16.1: Vector fields (pdf)
§16.2: Line integrals and work (pdf)
§16.3: Conservative vector fields (pdf)
§16.4: Green's theorem (pdf)
§16.5: Divergence and curl (pdf)
§16.5: Divergence and curl (3D) (pdf)
§16.6-7: Parametrization of surfaces (pdf)
§16.6-7: Surface area, surface integrals and flux (pdf)
§16.9: The divergence theorem (pdf)
§16.8: Stokes' theorem (pdf)
§16.8-9: Applications to Electromagnetism (optional) (pdf)
Course review (pdf)


Day Event
Sep 25 First lecture
Oct 18 First Midterm
Nov 11 No class: Veteran's day
Nov 13 Second Midterm
Nov 29 No class: Thanksgiving Friday
Dec 9 Final Exam

Textbook and Homework

The course textbook is Calculus: Early Transcendentals, 8th Edition, by James Stewart. Homework will be assigned and collected via Webassign. See here for instructions on how to purchase Webassign access along with an electronic copy of the course text. You are not required to purchase a physical copy of the textbook, even though the lectures will follow it quite closely.

Homework will generally be due at 11:00 p.m. on Thursdays. 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.

If you are having trouble with your access code, consider attending the "office hours" held by Webassign representatives on Tuesday, October 1 and Monday, October 7 from 11 a.m. to 3 p.m. at the Math Study Center (Communications Building, room B-014).

WebAssign login link: here.


Our course will have two midterm exams and one final exam. They will take palce in the room where the class meets for lectures. The midterm exams will be given on October 18 and November 13 during lecture. The final exam will take place on December 9 from 8:30 to 10:20 a.m.

Students may bring to exams a TI 30X IIS calculator and a 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 are 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 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.

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.