MATH 324 B, C
Advanced Multivariable Calculus

University of Washington, Winter 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.

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 3:30 to 5:00 p.m.

Time and place

Lectures take place on Mondays, Wednesday and Fridays at CHL 015.
Section B meets from 9:30 to 10:20 a.m.
Section C meets from 10:30 to 11:20 a.m.

Calendar and lecture notes

Day Topics
Jan 7 §15.1-2: Double integrals (notes)
Jan 9 §15.2-3: Double integrals, polar coordinates (notes)
Jan 11 §15.3-4: Polar coordinates, applications (notes)
Jan 14 §12.3-4, §15.5: Review of vectors, surface area (notes, supplementary notes)
Jan 16 §15.6: Triple integrals (notes)
Jan 18 §15.6-7: Cylindrical and spherical coordinates (notes, supplementary notes)
Jan 21 No class: Martin Luther King Day
Jan 23 §15.8: Change of coordinates (notes, supplementary notes)
Jan 25 §15.1-9: Review (notes)
Jan 28 First Midterm
Jan 30 §14.5-6: Chain rule, gradient vector (notes)
Feb 1 §14.6, §16.1: Gradient vector, vector fields (notes)
Feb 4 No class due to snow event
Feb 6 §16.2: Line integrals (notes)
Feb 8 §16.2: Line integrals (notes)
Feb 11 §16.3: Gradient fields (video lecture, notes, supplementary notes)
Feb 13 §16.3-4: Test for gradient fields, Green's theorem (notes)
Feb 15 §16.4: Green's theorem (notes)
Feb 18 No class: Presidents Day
Feb 20 §16.5: Divergence and curl (notes)
Feb 22 §14.5-6, §16.1-5: Review (notes)
Feb 25 Second Midterm
Feb 27 §16.5: Divergence and curl in 3D (notes)
Mar 1 §16.6: Parametrization of surfaces; tangent planes (notes)
Mar 4 §16.6-7: Surface area, surface integrals (notes)
Mar 6 §16.6-7: Surface area, surface integrals (see notes for March 4 and March 8)
Mar 8 §16.7: Surface integrals and flux (notes)
Mar 11 §16.9: The divergence theorem (notes)
Mar 13 §16.8: Stokes' theorem (notes, supplementary notes)
Mar 15 §15.1-9, §14.4-5, §16.1-10: Course review (notes)
Mar 18 Final Exam (section C)
Mar 20 Final Exam (section B)


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.

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, January 10 and Monday, January 14 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 January 28 and February 25 during lecture. Section B will have its final exam on March 20, from 08:30 to 10:20 am. Section C will have its final exam on March 18, from 08:30 to 10:20 am.

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 (January 28) 25%
Midterm 2 (February 25) 25%
Final Exam (March 18 or 20, depending on section) 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.