/ Math 20a

Math 20a: Calculus of several variables

Fall 2003

Instructor: Prof. Daniel Ruberman
E-mail: ruberman@brandeis.edu
Office: Goldsmith 310
Phone: 736-3074
Class schedule: Mon Wed Thu 9-10, Goldsmith 317.
Office hours: Monday 10-11, Wednesday 1-2, Thursday 10-11, and by appointment.
Textbook: Multivariable calculus (5th edition) by Stewart. (This may differ from the 4th edition in some respects; in particular, the numbering of the problems may not be the same.)

Syllabus

Chapter 11: Curves in the plane.
Chapter 13: Vectors in 3-dimensional space, surfaces.
Chapter 14: Vector functions (parametrized curves) in 3-space.
Chapter 15: Functions of several variables, derivatives, linear approximation, maxima-minima.
Chapter 16: Multiple integrals of functions of several variables, volume, surface area.
Chapter 17: Vector fields, line and surface integrals.

Exams, homework and grading

There will be 2 in-class midterm exams, 4 half-hour in-class quizzes and a 3-hour final exam. The schedule for the in-class exams and quizzes will be posted shortly; the final is Thursday December 4, 1:30 pm - 4:30 pm (Block B).
Homework will be assigned and collected weekly and will be graded and returned to you.
Grading formula:
Homework 15%
Quizzes 20%
Mid-term exams 35%
Final exam 30%

Web links

Homework assignments and solutions and review sheets will be available from this page. (Note: The homework assignments and review sheets have not yet been posted. Please check back at the beginning of the semester.) Some of this will be in pdf format, for which you will need the free Acrobat Reader.
Here is a short list of trigonometric identities.
Here is a tool for integrating.
Here is the chart showing some critical points and their Hessians, from class on November 12.
Here is some graphing software you may find useful. Just click on the link to download a compressed copy. They are freeware.
- For those with Macs, check out the graphing calculator which is included.
- For graphing functions of one-variable (curves in the (x,y)-plane), click here (Mac only).
- For graphing functions of two variables (surfaces in (x,y,z)-space) click here for the Mac version, or here for the Windows version.

Exam schedule and solution sheets

Event	Date	Text sections	Solutions	Mean Grade
Quiz 1	Sept. 24	11.1-5, 13.1	Given in class	93%
Quiz 2	Oct. 9	Through 13.6	Given in class	85%
Quiz 3	Nov. 6	Through 15.4	Given in class	84%
Quiz4	Nov. 24	Through 16.2
Exam 1	Oct. 16	Through 14.4	Handout	83%
Exam 2	Nov. 13	Through 15.6		88%
Final	Dec. 4, 1:30-4:30

Lecture notes from November 26 class.

Homework assignments and solutions

In addition to the even-numbered homework, which are to be handed in for grading, I have suggested some odd-numbered problems for you to do for practice. The solutions to these are in the back of the book, so they won't be graded; you can write the solutions on the same paper as the even ones if you find that to be convenient. Problems given by letters A, B, C, etc. are to be accessed by clicking. Solutions will be posted after the problems are turned in, and are accessed by clicking the orange buttons.

No. Date due Sections to read Problems Solutions

1
Sept. 11 11.1-3 11.1: # 2, 6, 10.
11.2: # 2, 6, 16, 32, 42.
11.3: # 4, 8, 14, 18, 26, 56, 68.

2 Sept. 18 11.4, 13.1 11.4: # 2, (3), 6, (11), 12, (25), 26, (47), 48.
13.1: # (3), 4, (13), 14, 16, (33), 42.

3 Sept. 25 13.2, 13.3 13.2: # 4, (5), 6, (15), 16, 18, 26, (27), 30.
13.3: # 6, (7), (11), 12, (21), 22, 24, 36, 44, (45), 46, 50.

4 Oct. 2 13.4, 13.5,13.6 13.4: 6, (7), (15), 16, (21),22,(29), 30, (41), 42.
13.5: 4, 10, (23), 24, (41), 42.
13.6: 2, (9), 10, (13), 14, (17), 20, (41), 42.

5 Oct. 9 14.1, 14.2 14.1: (5,13) 14, 16, (19-24).
14.2: (5), 6, 12, (15), 16, 18, 22, 24, (31), 32, 34, (41) 44.

6 Oct. 15 14.3, 14.4 14.3: (3), 4, 6.
14.4: (5), 6, 12, (15), 16, (19), 20, 22, (23).

7 Oct. 23 13.7, 15.1, 15.2 13.7 10, (11), (21), 22, (31-36), 38, 44, 52, (53).
15.1: 6, (17), 26, (27), (28), (30), 34, (43), 44, (53-58), 60.
15.2: (1), 6, (7), 10, 18, (27), 28, 32, (33).

8 Oct. 30 15.3, 15.4 15.3: (5,6), 8, (15), 16, 24, (29), 32, (41), 42, (53), 56, (68,69, 71,77).
15.4: 4, 12, (13), (19), (23), 24, 30.

9
Nov. 6
15.5
15.5: (3), 4, 6, 8, 12, (21), 22, 24, (27), (31), 34, 38,(39), 40, (45), 46, (47)

10 Nov. 12 15.6 15.6: (7), 8, 16, 22, (23), (27), 28, 32, (37), 38, 42, (55), (61)

11
Nov. 20 15.7 (through p. 994)
16.1, 16.2 15.7: (1), 2, 4, (7), 8, 12, 18
16.2: 2, (11), 12, 16, 24, (25), 28.

12
Dec. 1 16.3
16.4
16.7 16.3: (1), 2, 4, 6, (11), 14, 20, (25), 28, (43), 44.
16.4: (7), 8, 10, (15), 22, 26, 28, (36--this is a very important integral!).
16.7: 4, (7), 8, 10, (19), 20.

No.	Date due	Sections to read	Problems
1	Sept. 11	11.1-3	11.1: # 2, 6, 10. 11.2: # 2, 6, 16, 32, 42. 11.3: # 4, 8, 14, 18, 26, 56, 68.
2	Sept. 18	11.4, 13.1	11.4: # 2, (3), 6, (11), 12, (25), 26, (47), 48. 13.1: # (3), 4, (13), 14, 16, (33), 42.
3	Sept. 25	13.2, 13.3	13.2: # 4, (5), 6, (15), 16, 18, 26, (27), 30. 13.3: # 6, (7), (11), 12, (21), 22, 24, 36, 44, (45), 46, 50.
4	Oct. 2	13.4, 13.5,13.6	13.4: 6, (7), (15), 16, (21),22,(29), 30, (41), 42. 13.5: 4, 10, (23), 24, (41), 42. 13.6: 2, (9), 10, (13), 14, (17), 20, (41), 42.
5	Oct. 9	14.1, 14.2	14.1: (5,13) 14, 16, (19-24). 14.2: (5), 6, 12, (15), 16, 18, 22, 24, (31), 32, 34, (41) 44.
6	Oct. 15	14.3, 14.4	14.3: (3), 4, 6. 14.4: (5), 6, 12, (15), 16, (19), 20, 22, (23).
7	Oct. 23	13.7, 15.1, 15.2	13.7 10, (11), (21), 22, (31-36), 38, 44, 52, (53). 15.1: 6, (17), 26, (27), (28), (30), 34, (43), 44, (53-58), 60. 15.2: (1), 6, (7), 10, 18, (27), 28, 32, (33).
8	Oct. 30	15.3, 15.4	15.3: (5,6), 8, (15), 16, 24, (29), 32, (41), 42, (53), 56, (68,69, 71,77). 15.4: 4, 12, (13), (19), (23), 24, 30.
9	Nov. 6	15.5	15.5: (3), 4, 6, 8, 12, (21), 22, 24, (27), (31), 34, 38,(39), 40, (45), 46, (47)
10	Nov. 12	15.6	15.6: (7), 8, 16, 22, (23), (27), 28, 32, (37), 38, 42, (55), (61)
11	Nov. 20	15.7 (through p. 994) 16.1, 16.2	15.7: (1), 2, 4, (7), 8, 12, 18 16.2: 2, (11), 12, 16, 24, (25), 28.
12	Dec. 1	16.3 16.4 16.7	16.3: (1), 2, 4, 6, (11), 14, 20, (25), 28, (43), 44. 16.4: (7), 8, 10, (15), 22, 26, 28, (36--this is a very important integral!). 16.7: 4, (7), 8, 10, (19), 20.