# Calculus of Several Variables

## Virtual Spring Semester 2021

Virtual Instructor: Matt Kerr, matkerr [at] wustl.edu
Office: there is no office, only Zoom
Zoom Office Hours: 1-1:45 M, 8-9pm Tu, 4:45-5:30 F

Course Outline:

We will study the differential and integral calculus of functions in n-space, making some use of matrix algebra. The level is in between that of Calculus III and the upper-level analysis courses. Towards the end, we will do a bit on differential forms and integration on manifolds.

Prerequisites: Math 233 and 309

Class and Exam Schedule:

Lectures are on Tu/Th from 8:30-9:45am, on Zoom. The first class is on Tuesday Jan. 26 and the last class is on Tuesday May 4. There is no class on Tuesday Feb. 9 or Tuesday Mar. 2 (study/wellness days).

Midterm Exam 1: Monday March 1 (take home)
Midterm Exam 2: Wednesday April 7 (take home)
Final Exam: Monday May 10

The final exam is currently presumed to be a take-home exam as well, due on May 10. If the virus situation changes and we are in person, it will take place on this date from 8:30pm-10:30pm.

Assignments:

These will be due, via PDF upload to Canvas, on Wednesdays at noon. Solutions will also be posted on Canvas and may include students' work. I encourage you to visit my office hours to discuss problem sets, and to form study groups to discuss the more difficult problems (though solutions must be written up independently).

HW #1 (due Feb. 3): §1.2: #1g, 2g, 7, 14, 15; §1.3: #1abhi, 3, 9; §1.4: #1acij, 2a, 7, 11, 13, 25; §1.5: #6b, 7b, 9, 13.
HW #2 (due Feb. 10): §2.1: #2, 9bd, 11a, 12ab; §2.2: #1bdf, 4, 7, 9, 14; §2.3: #1, 2, 7, 8abci, 13, 15
HW #3 (due Feb. 17): §3.1: #1bf, 2c, 3b, 8, 9, 10b; §3.2: #2b, 3d, 7, 9, 10, 15; §3.3: #2, 3, 4b, 8, 11, 14
HW #4 (due Feb. 24): §3.4: #1c, 2c, 4, 7, 11; §3.5: #2, 4, 5, 7b, 9; §3.6: #1, 2ab, 3b, 7, 9; §4.1: #3bdh, 4ac
HW #5 (due Mar. 10): §4.1: #6b, 12b, 17; §4.2: #2bd, 3c, 7; §4.3: #1, 2df, 3, 5, 11, 14c; §4.4: #3be, 6, 9, 13, 14
HW #6 (due Mar. 17): §4.5: #2, 3, 5, 6, 7; §5.1: #1bdfg, 2, 4b, 8, 11, 12; §5.2: #1bfh, 2, 4, 9, 12
HW #7 (due Mar. 24): §5.3: #1bhij, 2, 4, 5; §5.4: #6, 15, 20, 24, 29b, 30a; §5.5: #1ab, 2, 3ab, 4
HW #8 (due Mar. 31): §5.5: #5ab, 7ab, 12d, 13ab; §6.1: #2, 6, 7, and this; §6.2: #1bd, 2ab, 3bd; §6.3: #5abc, 6, 7bc, 10, 12
HW #9 (due Thurs. Apr. 15): §7.1: #2, 6, 7; §7.2: #8b, 10, 21; §7.3: #7, 11, 14; §7.4: #2, 19, 25; §7.5: #1ac, 2, 7
HW #10 (due Apr. 21): §7.5: #9, 12, 19; §7.6: #4b, 8, 11, 15; §8.2: #2, 5, 7abc, 8bc, 11e, 14, 16; §8.3: #1bd, 3ab
HW #11 (due May 3): §8.3: #6ab, 8, 9, 13; §8.4: #1, 6, 7, 17; §8.5: #2, 7, 9; §8.6: #6, 9, 10

Grader: Di Wu, wu.di [at] wustl.edu
Books:

Theodore Shifrin, Multivariable Mathematics, Wiley, 2005

is the text for this class. You should have your own copy because the homework assignments will come from here, and we will mostly follow it in lectures.

Lectures and Quizzes:

In the calendar below I will post my slides for each lecture, after the class takes place. Click on the "Lec X" link (once it is active) for the notes. The sections covered in the lecture will also be displayed in the table (though these sections may not be covered in full). The "week of" date refers to Monday.

The lecture notes are intended to help you prepare for exams, fill in bits you may have missed in lecture, or even avoid taking notes altogether. They are not intended, however, as a substitute for class attendance and reading the book.

Week of ... Mon Tue Wed Thu
Jan. 25 [Lec 1] 1.1-1.4 [Lec 2] 1.4-1.5
Feb. 1 [Lec 3] 2.1-2.2 HW 1 [Lec 4] 2.2-3.1
Feb. 8 Study day
(no class)
HW 2 [Lec 5] 3.2-3.3
Feb. 15 [Lec 6] 3.4-3.5 HW 3 [Lec 7] 3.6-4.1
Feb. 22 [Lec 8] 4.1-4.2 HW 4 [Lec 9] 4.2-4.3
Mar. 1 Exam 1
due
Wellness Days [Lec 10] 4.4
Mar. 8 [Lec 11] 4.5 HW 5 [Lec 12] 5.1-5.2
Mar. 15 [Lec 13] 5.3-5.4 HW 6 [Lec 14] 5.4-5.5
Mar. 22 [Lec 15] 5.5-6.1 HW 7 [Lec 16] 6.2-6.3
Mar. 29 [Lec 17] 7.1-7.2 HW 8 [Lec 18] 7.2-7.3
Apr. 5 [Lec 19] 7.3-7.5 Exam 2
due
[Lec 20] 7.5
Apr. 12 Wellness
Day
[Lec 21] 7.6-8.2 HW 9 [Lec 22] 8.2-8.3
Apr. 19 [Lec 23] 8.3 HW 10 [Lec 24] 8.4
Apr. 26 [Lec 25] 8.5 [Lec 26] 8.6
May 3 HW 11 [Lec 27] 8.7
+ Final Review
No
Class

Homework and examination grades will be regularly updated on Canvas. Your final grade for the semester is determined as follows: HW 40%, midterms 30%, final exam 30%. I will drop the lowest two grades you receive on homework.

Curving and grade scale: In the event that the average score on any exam is less than 75%, all exam scores will be adjusted upward by adding a constant to everyone's score (so that the average is 75%). No adjustment is made if the average is above 75%. The grade scale is as follows:

A+ A A- B+ B B- C+ C C- D F
TBA 90+ [85,90) [80,85) [75,80) [70,75) [65,70) [60,65) [55,60) [50,55) [0,50)

The Pass/Fail policy is that you must get at least a C- to earn a "Pass".

If you are unable to take a midterm exam due to illness or family emergency, please let the instructor know before the duedate. In this case, your grade will be calculated from the homework and other taken exams. The final exam must be taken to complete the class; if one of the above reasons prevents you from taking it, you will receive an Incomplete and will have to make up the exam later to resolve this.

This link takes you to the standard university policies on academic integrity.