Multivariate Calculus - MA225 - Spring 2015 Course Home Page

Course: MA225 B, Multivariate Calculus
Professor: Jared Weinstein
TA: Ben Fischer
Lecture B1: TR 2-3:30, CAS 313
Section B2: W 10-11, MCS B21
Section B3: W 11-12, MCS B33
Section B4: R 10-11, CAS 220
Section B5: R 11-12, MCS B23
Office hours: M 10-11, W 11-12, MCS 227
TA Office hours: T 1-2, 3:30-4:30, MCS 258

Course Overview

This course is mostly about calculus in three dimensions, so we'll start with vectors, lines, and planes in 3D. Then we cover partial derivatives, directional derivatives, multiple integration, cylindrical and spherical coordinates. The last and most interesting chapter covers the big theorems of integration of vector fields (Green's theorem and Stokes' theorem).

Text

Calculus, Early Transcendentals, by Briggs and Cochran. The physical textbook is all you need -- I won't be requiring any additional software.

Discussion sections

You must be enrolled in one of the discussion sections for the course (B2, B3, B4, B5). The sections will be used for going over lecture material and assignments in a way that is less structured than the lectures. You will be able to raise questions and see examples worked out in detail. All homework will be collected during discussion sections.

Assignments

In this course, there will be new concepts rolled out with every lecture that build directly on the previous ones. Falling behind and then cramming for the exam is seriously discouraged. The homework assignments are in place to make sure you are keeping pace with the lectures.

Homework assignments are due in discussion section every week, with the exception of the first week. The assignments are posted in the table below. You are allowed and encouraged to work together on homework assignments, but you must hand in solutions which are written in your own words. Select problems from each assignment will be graded and returned to you the following week.

Your lowest two homework scores will be dropped, but in return, I am not going to accept any late homeworks, no exceptions. This policy is intended to accommodate emergencies, so you shouldn't use this policy to skip two assignments of your choice.

Exams

The dates for the exams are as follows.

 Midterm I Tuesday, Mar. 3, 2015, during lecture Midterm II Tuesday, Mar. 31, 2015, during lecture Final Exam Wednesday, May 6, 2015, 3-5, location TBA

You must take the final exam to pass the class.

If you feel one of your exams was ncorrectly graded, then you must bring it to my attention within one week of receiving it. While grading mistakes do happen, I generally do not accede to requests for more partial credit.

The course grade will be based on the following formula: Homework 20%, Midterm I 20%, Midterm II 20%, Final exam 40%. I will compute this weighted average of your raw homework and exam scores to come up with a number, your final score in the class. Once everyone's final scores are computed, I will decide the cutoffs that determine letter grades (that is, the curve). I won't know exactly what the curve is until after the final exam.

How to do well in this class

Probably my least favorite thing about teaching calculus is when a student comes to my office in the final week of class and asks what can be done to improve his or her performance on the final. At that point, there is little I can do to help. Worse yet, I get the impression from such students that my class is little more than a letter grade to them, and that I am a barrier to their preferred grade. This sets up a somewhat adversorial relationship between student and professor, and you probably want to avoid that.

Conversely, one of my favorite things is getting a visit from a student in the first weeks of class who wants to say hello, tell me about their background with math, and ask how to get on the right track to succeed. This sets up a cooperative student-professor relationship. Here is a list of suggestions for how to do well:

• Come to class, pay attention, and ask loads of questions during lecture. I love getting questions. I really love it when students correct the stupid mistakes I make while lecturing (there will be plenty of these).
• Do all the homework problems.
• Come to my office hours. Alas, I find that the most frequent visitors to my office hours are the students who need help the least. The TA will also hold office hours.
• Go to the tutoring room in MCS B24 between 10 and 4 for help from our graduate students. More info here.

Table of assignments

Sections take place on Wednesdays and Thursdays, so I've listed both as the due dates for the assignments.

HW Assignment Due
#1 §11.1: 12, 15, 19a-d, 32, 44, 49, 84.
§11.2: 15, 18, 29, 50, 58.
§11.3: 9, 12, 20, 25, 40, 73a.
Jan. 28/29
#2 §11.4: 9, 11, 29, 54, 55.
§11.5: 9, 14, 22, 49.
§11.6: 13, 17, 62, 66.
Feb. 4/5
#3 §11.8: 9, 28, 46.
§12.1: 11, 16, 26, 41, 53, 63.
§12.2 (optional): 4, 17, 27, 37.
Feb. 11/12
#4 §12.3 17, 22, 25, 26, 56.
§12.4 10, 16, 48, 54.
Feb. 18/19
#5 §12.5 7, 15a, 23, 55.
§12.6 15, 18, 27, 45.
§12.7 9, 24, 31, 43.
Feb. 25/26
#6 §12.8 15, 20, 25, 33, 37.
§12.9 5, 15, 19, 52a.
Mar. 4/5
#7 §13.1 5, 34, 40.
§13.2 13, 24, 49, 72d.
§13.3 11, 23, 27, 61
§13.4 13, 20, 23, 57
Mar. 18/19
#8 §13.5 29, 39, 70
§13.6 15, 16, 45
§13.7 27, 31, 46, 47, 48, 49
Mar. 25/26
#9 §14.1 2, 9, 16, 25, 29, 46. Apr. 3 (in MA 225 mailbox)
#10 §14.2 11, 14, 15, 47, 48,
§14.3 11, 14, 15, 26, 33
Apr. 8/9
#11 §14.4 4, 11, 16, 17, 23, 28, 29, 60
§14.5 9, 21, 27, 41, 44, 46, 54, 57, 61
Apr. 15/16
#12 §14.6 12, 27, 30, 59
§14.7 1, 2, 5, 10, 11, 25, 37, 40a-b
Apr. 22/23