MATH 324 D
Advanced Multivariable Calculus

University of Washington, Spring 2019

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.


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: Chemistry Library Building, Room 015 (CHL 015)

Calendar and lecture notes

Day Topics
April 1 §15.1-2: Double integrals (notes)
April 3 §15.2,4: Double integrals, applications (notes)
April 5 §15.3-4: Polar coordinates, applications (notes)
April 8 §12.3-4, §15.5: Review of vectors, surface area (notes, supplementary notes)
April 10 §15.6: Triple integrals (notes)
April 12 §15.6-7: Triple integrals and cylindrical coordinates (notes)
April 15 §15.8: Spherical coordinates (notes)
April 17 §15.8: Change of coordinates (notes)
April 19 §15.1-9: Review (notes)
April 22 First Midterm
April 24 §14.5-6: Chain rule, gradient vector (notes)
April 26 §14.6, §16.1: Gradient vector, vector fields (notes)
April 29 §16.2: Line integrals (notes)
May 1 §16.2: Line integrals (notes)
May 3 §16.3: Gradient fields (notes, supplementary notes)
May 6 §16.3-4: Test for gradient fields, Green's theorem (notes)
May 8 §16.4: Green's theorem (notes, supplementary notes)
May 10 §16.5: Divergence and curl (notes)
May 13 §14.5-6, §16.1-5: Review (notes, old second midterm, solutions)
May 15 Second Midterm
May 17 §16.5: Divergence and curl in 3D (notes)
May 20 §16.6: Parametrization of surfaces; tangent planes (notes)
May 22 §16.6-7: Surface area, surface integrals (notes)
May 24 §16.7: Surface integrals and flux (notes)
May 27 No class: Memorial Day
May 29 §16.9: The divergence theorem (notes)
Mar 31 §16.8: Stokes' theorem (notes)
June 12 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 Fridays. 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 Thursday, April 4 and Monday, April 8 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 CHL 015, the room where our class will meet for lectures. The midterm exams will be given on April 22 and May 15 during lecture. The final exam will take place on June 12 from 2:30 to 4:20 p.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 (due Fridays) 10%
Midterm 1 (April 22) 25%
Midterm 2 (May 15) 25%
Final Exam (June 12) 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.