MATH 20a: Calculus of Several Variables - Fall 2005

Instructor	Mario O. Bourgoin	Office	Goldsmith 303
Email	mob@brandeis.edu	Phone	x6-3072

Description

This course builds upon and extends MATH 10a and 10b. Topics include vectors and vector-valued functions, partial derivatives and multiple integrals, extremum problems, line and surface integrals, Green's and Stokes's theorems. The course emphasizes techniques and applications over theory.

Textbook

Multivariable Calculus, 5th edition, by James Stewart

Syllabus

Ch. 11: Curves in the plane, §§1-3.
Ch. 13: Vectors in 3-dimensional space, surfaces, §§1-7.
Ch. 14: Vector functions (parametrized curves) in 3-space, §§1-3.
Ch. 15: Functions of several variables, derivatives, maxima-minima, §§1-7.
Ch. 16: Multiple integrals of functions of several variables, volume, surface area, §§1-8.
Ch. 17: Vector fields, line and surface integrals, §§1-9.

Evaluation

Homework (10%): Weekly homework assignments.
Quizzes (15%): 3 half-hour in-class quizzes (Sep. 21, Oct. 27, Nov. 30).
Midterms: (40%): 2 evening midterm exams (Oct. 10, Nov. 10, Pollack, 7:30 PM-9:30 PM).
Final (35%): 1 final (Block D: Fri. Dec. 16, 1:30 PM-4:30 PM).

Grading

	F		D-		D		D+		C-		C		C+		B-		B		B+		A-		A
0		60		63		67		70		73		77		80		83		87		90		93		100

Policies

DEADLINES. All deadlines are to be respected. Make ups will only be allowed for pre-arranged absences due to documented medical reasons.

STUDENTS WITH DISABILITIES. If you are a student who needs academic accommodations because of a documented disability you should contact Professor Bourgoin and present your letter of accommodation as soon as possible. If you have questions about documenting a disability or requesting academic accommodations you should contact Beth Rodgers-Kay in Undergraduate Academic Affairs at 6-3470. Letters of accommodations should be presented at the start of the semester to ensure provision of accommodations. Accommodations cannot be granted retroactively.

Schedule
Our class normally meets Monday, Wednesday, and Thursday, from 11:10 AM through Noon. In the schedule below, days with classes have their text in bold font.

Monday
Tuesday
Wednesday
Thursday
Friday

Sep 1 First
2

5 Holiday
6
7
8
9

12
13
14
15
16

19
20
21 Quiz
22
23

26
27
28
29
30

Oct 3 Tuesday
4 Holiday
5 Holiday
6
7

10 Midterm
11
12
13 Holiday
14 Drop Day

17
18 Holiday
19
20
21

24
25 Holiday
26
27 Quiz
28

31
Nov 1
2
3
4

7
8
9
10 Midterm
11

14
15
16
17
18 Drop Day

21
22
23 See Below
24 Holiday
25

28
29
30 Quiz
Dec 1
2

5
6
7
8
9

12 Last
13
14 15 16 Final

* The Wednesday 11/23 11 AM class will be held on Sunday 11/20 3PM in Goldsmtih 317.

Quizzes, Midterms, and Final
Quizzes cover the material seen since the previous quiz while the midterms and final are cumulative. Students may bring one 3x5 card of notes for the first midterm, two cards for the second, and three cards for the final. Calculators are allowed for all examinations, however they may not be so powerful as to do the work for you.

Exam Classes Covered Exam Classes Covered

Quiz 1
Sep. 21
From Sep. 1 Thru Sep. 19
Midterm 1
Oct. 10
From Sep. 1 Thru Sep. 29
Practice Exam and Solutions

Quiz 2
Oct. 27
From Oct. 6 Thru Oct. 24
Midterm 2
Nov. 10
From Sep. 1 Thru Nov. 3
Practice Exam and Solutions

Quiz 3
Nov. 30
From Nov. 7 Thru Nov. 28
Final
Dec. 16
From Sep. 1 Thru Dec. 12
Practice Exam and Solutions

Homework
IMPORTANT NOTE: Problems numbers that are in parenthesis are not graded though they may be handed in on the same sheet as the graded problems. They are listed because they may provide clues to solving other problems or provide some idea that is useful but not required for class.

Assignments are to be handed in on the dates given below, whether there is a class or not. All pictures and graphs should carefully be drawn on graph paper. Solutions to an assignment will be posted here after it is handed in. Before calculating your final homework grade, you two lowest homework grades will be dropped.

Date
Assignment
Date
Assignment

Mon Sep 12 Noon
11.1: 8, 12, 16, (23), 24
11.2: 4, 16, 42, 60, (67)
Solutions
Tue Nov 1 1PM 15.1: (1), 6 , 14, 54-58 (even), 60
Solutions

Mon Sep 19 Noon 11.3: 6, 10, 20, 26
13.1: 4, 12, 18, 32
Solutions Tue Nov 8 1PM 15.2: 6, 10, 12, 18, 28
15.3: (5), 8, 10 (no plots), 16, (24), (30), (36), 42, 56, (62), 66, 68, (69), (70)
Solutions

Mon Sep 26 Noon 13.2: 4, 16, 22, 28
13.3: 6, (11), 12, 20, 24, 40, 48, 50
Solutions Tue Nov 15 1PM 15.4: 6, 12, (19), 24, (28), 30
15.5: 4, (6), 8, (10), (13), 14, 22, (27), (31), 32, 38, (40), 46
Solutions

Mon Oct 3 Noon
No Class
13.4: 4, (9), 24, 30, 36, (21), (39), 41
13.5: 8, (14), 32, (52), (63), (66)
13.6: 8, (9), 10, 21-28 even, 34
Solutions Tue Nov 22 1PM 15.6: 2, 10, 12, 22, (27), 28, 34, (37), 38, 42, (53), (61)
15.7: 2, 4, 6, (13), 18, (29), 30, (43), 44
Solutions

Mon Oct 17 Noon 13.5: 48, 54, 64, 68
13.7: 10, (20), (24), 30, 44, 52
Solutions Wed Nov 30 1PM 16.1: (11), 12, (13), 14
16.2: (3), 6, 12, 16, 18, 24, 28
16.3: 2 ,4, 6, (11), 14, 20, (25), (46)
Solutions

Wed Oct 26 1PM
14.1: (1), 4, 12, 20-24 (even), (33), (39), 40, (41)
14.2: 2, (18), (22), 26, 32, 34, (42), (45), 46, (48), (49)
14.3: 6, 10
Solutions Wed Dec 7 1PM 16.4: 8, 16 (hint: subtract one integral from the other), 26
16.5: 2
16.7: 4, 8, 10, 32 (only do dxdydz)
16.8: 2, (6), 10, 18, 30
Solutions

Wed Dev 14
1 PM
Extra Credit
17.1: 11-18 even, 29-32 even, (33), 34
17.2: 2, 6, 8, 10, 16, 18, 20
Solutions