MATH 324 F
Advanced Multivariable Calculus

University of Washington, Spring 2020


Name: Lucas Braune
E-mail: lvhb 'at'

Course organization at a glance

For more information, please see below.

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)

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.

Update: Cengage is offering FREE WebAssign access to UW students this Spring quarter. Here are the instructions provided by a Cengage representative.

Homework will generally be due at 11:00 p.m. on Fridays. If you need an extension on the first homework assignment, which is due Tuesday of the second week of class, please send me an e-mail. From the second assignment onwards, extensions will not 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.


Our course will have two midterm exams and one final exam. Students will complete these exams online on Gradescope, where they will view exam questions and upload pictures of their handwritten work.

Students should sign up for Gradescope using their UW e-mail address, student number and preferred name, as they appear on MyUW. The course entry code is 92Y47R.

Some recommendations to students regarding Gradescope:

The midterm exams will be given on Monday, April 20 and Friday, May 15. Each exam will be made available on Gradescope at 9:30 a.m. Students will have one hour or until 11:00 a.m. to complete the exams, whichever is sooner.

The final exam will be given on Wednesday, June 10 (the date set by the University). The exam will be made available on Gradescope at 8:30 a.m. Students will have two hours or until 11:00 am to complete the exam, whichever is sooner.

Students experiencing technical difficulties and unable to submit their work through Gradescope should e-mail their answers to the instructor. After doing so, they should contact the instructor to explain their situation. Exam solutions submitted after the time limit will be subject to grade penalties.

During online exams, students may consult

Students may NOT consult other sources such as

The number of pages in the notesheet is limited only to prevent students from cataloguing the answers to a large number of questions from old exams.

At the beginning of each exam students will be asked to copy and sign a short honor statement: “I affirm that I will not give or receive any unauthorized help on this exam, and that all work will be my own.” Regarding the possiblity that some students will not uphold this honor statement:

As a general policy, make-up exams will not be given. If you miss an exam due to unavoidable, compelling, and well-documented circumstances, including technical difficulties, 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.

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


Each student's course grade will be computed from the average of the student's percentage scores on the homework, midterms, and final, with the weights shown below. The average percentage score will be converted into a 4.0 scale by a piecewise linear function.

Homework 10%
Midterm 1 30%
Midterm 2 30%
Final Exam 30%


Week Starts Topics Events
1 Mar 30 Double integrals
2 Apr 6 Review of vectors
The area of a graph
Triple integrals
T: WebAssign 15.1-3 due
F: WebAssign 15.4-6 due
3 Apr 13 Cylindrical & spherical coords
Change of coordinates
F: WebAssign 15.7-9 due
4 Apr 20 Chain rule
Vector fields
M: Midterm 1
F: WebAssign 14.5-6 due
5 Apr 27 Line integrals F: WebAssign 16.1-2 due
6 May 4 FTC for line integrals
Green's theorem
F: WebAssign 16.3-4 due
7 May 11 Green's theorem
Divergence and curl
Th: WebAssign 16.5 due
F: Midterm 2
8 May 18 Parametrization of surfaces
Surface area
F: WebAssign 16.6.I-II due
9 May 25 Surface integrals, flux M: Memorial day
F: WebAssign 16.7.I-II due
10 Jun 1 The divergence theorem
Stokes' theorem
F: WebAssign 16.8-9 due
11 Jun 8 W: Final Exam

M = Monday, T = Tuesday, W = Wednesday, Th = Thursday, F = Friday