# MATH 324 FAdvanced Multivariable Calculus

University of Washington, Spring 2020

#### Instructor

Name: Lucas Braune
Website: http://math.uw.edu/~lvhb
E-mail: lvhb 'at' uw.edu

#### Course organization at a glance

• Lectures will be prerecorded and posted on Panopto (course folder) and Youtube (playlist) at a rate of three per week. Students are encouraged to watch the lectures near the time slot reserved for our class (MWF 9:30-10:20 am).
• We will have virtual office hours on Zoom (meeting link) Mondays and Thursdays from 4 to 5 pm, and by appointment.
• Students will complete exams online on Gradescope (link), where they will see exam questions and upload pictures of their handwritten work.

#### 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.

#### Exams

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:

• Try using Gradescope on your smartphone. On some devices, the "Select file(s)" button on Gradescope gives the user the option to open the device's camera app. This makes the process of uploading pictures mostly frictionless.
• Use the assignment "Sample Midterm 1" to familiarize yourself with the platform. This assignment will not be graded.

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

• the lecture notes provided by the instructor (available in two parts: part 1 and part 2),
• a note sheet (one page, handwritten on both sides), and
• a nongraphing calculator.

Students may NOT consult other sources such as

• other people, or
• the internet.

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:

• For now, we will NOT adopt an online proctoring service such as Proctorio. We may use such a service in the future, although I hope that won't be necessary.
• Student handwriting may be compared across exams, and students may be asked to give oral explanations of their solutions via Zoom.
• Certain websites that cheaters might use to request help on exam questions will be monitored. Please note that consulting such websites during exams is not risk-free.
• To help ensure that students who abide by the rules do not have to worry about whether others are doing the same, in this class students will not be graded against each other. When choosing the curve used to compute course grades at the end of the quarter, my priority will be to ensure that students with a given performance on graded assignments receive this quarter a course grade that is no lower than what the same performance would have guaranteed in previous quarters.

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%

#### Schedule

Week Starts Topics Events
1 Mar 30 Double integrals
Applications
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