Calculus of Several Variables (Math 22)
Spring 1999, UCSC

Lecture Sections
Thim Lecture 1 M W F, 8-9:10pm 11P: T TH 10-11:50am Applied Sci 268.
12P: M W 2-3:50pm Applied Sci 268.
13p: M W 4-5:50pm Applied Sci 295.

Instructor
Professor Mohammad Ghomi Check instructor's web site periodically for revised versions of this syllabus, and to obtain copies of old tests and quizzes.

Teaching Assistants
Don Kim, and Kirk Lackey The section assignments for each TA are as follows: Don, Section 12p; Kirk, Sections 11P and 13P.

Course Description
Continuation of Calculus 19B. Study of derivatives and integrals of functions of several variables. For a list of topics see the Lecture and reading schedule below.

Prerequisites
Calculus 19B--a sound understanding of derivatives and integrals of functions of one variable.

Textbook
Calculus Early Transcendentals, by J. Stewart, Third Edition.

Homework and Quizzes
There will be weekly homework assignments to be turned in to the teaching assistants. Students in M-W sections will turn in their homework on Wednesdays, and students in T-Th sections will turn in their homework on Thursdays. Late homeworks will not be accepted. Also, there will be weekly quizzes. Students in M-W sections will take their quizzes on Mondays, and students in T-Th sections will take their quizzes on Tuesdays.

Lecture and Reading Schedule
We will cover chapters 11, 12, and 13 of the textbook. The lecture schedule appears below. You should try to read the sections, or at least glance at them, before coming to class.
Dates Lectures
March
April		 31
2		 W
F		 11.1
11.2		 Three dimensional coordinates
Vectors
April 5
7
9		 M
W
F		 11.3
11.4
11.5		 Dot product
Cross product
Lines and planes
12
14
16		 M
W
F		 11.6
11.7
11.8		 Quadric surfaces
Vector Functions and Space curves
Arc length and Curvature
19
21
23		 M
W
F		 11.9
11.10
12.1		 Motion in Space: Velocity and Acceleration
Cylindrical and Spherical coordinates
Functions of several Variables
26
27
30		 M
W
F		 12.2
12.3
.		 Limits and Continuity
Partial Derivatives
Review
May 3
5
7		 M
W
F		 .
12.4
12.5		 Midterm (covers up to 12.2)
Tangent planes and Differentials
The chain rule
10
12
14		 M
W
F		 12.6
12.7
12.8		 Directional derivatives and Gradient
Max and Min
Lagrange Multipliers
17
19
21		 M
W
F		 13.1
13.2
13.3		 Double integrals over rectangles
Iterated integrals
Double integrals over general regions
24
26
28		 M
W
F		 13.4
13.5
13.6		 Double integrals in polar coordinates
Appications of double integrals
Surface area
June 1
2
4		 T*
W
F		 13.7
13.8
.		 Triple integrals
Triple integrals in cylindrical and spherical coordinates
Review
7 M . Final (Comprehensive)

* Exchange day (Monday classes will meet on Tuesday).

Assignments
The following are the homework assignments for the first two weeks. The rest will be announced later, and will be posted on this website. You should plan to work on these problems over a period of several days. Getting a head start on each assignment is perhaps the most critical factor determining your success in this class.
Homework # Due Date Problems
1 Apr 7/8 11.1) 2, 8, 12, 18, 24, 36, 40, 46;
11.2) 4, 12, 16, 20, 28, 36;
11.3) 8, 9, 14, 22.
2 Apr 14/15 11.3) 38, 43, 52, 54, 62;
11.4) 4, 8, 12, 15, 20, 22, 26, 30;
11.5) 2, 6, 20, 24, 28, 36, 44, 55;
11.6) 2, 6.
3 Apr 21/22 11.6)18, 22, 26, 44;
11.7)2, 6, 8, 10, 24, 36, 38, 49;
11.8)4, 12, 18, 24, 32, 34.
4 Apr 28/29 11.9)4, 6, 10, 14, 18, 20;
11.10)4, 10, 16, 22, 26, 30, 36, 40, 54, 63;
12.1)4, 6, 12, 16, 34, 40, 44, 54.
5 May 5/6 12.2)6, 8, 12, 16, 30, 36, 44, 49;
12.3)2, 6, 10, 20, 49, 50, 57, 91.
6 May 12/13 12.4)2, 4, 12, 16, 20, 22, 24, 26, 30, 32;
12.5)2, 6, 8, 14, 20, 26, 30, 34, 38.
7 May 19/20 12.6)2, 6, 10, 18, 24, 26, 36, 48;
12.7)2, 8, 20, 26, 30, 36, 48, 50;
12.8)4, 8, 16, 20, 23.
8 May 26/27 13.1)1, 4, 8, 14, 16;
13.2)4, 10, 20, 26, 28, 36;
13.3)4, 10, 18, 20, 24, 36, 42.
9 June 2/3 13.4)2, 4, 16, 32, 22;
13.5)2, 4, 8, 14, 16;
13.6)2, 6, 8, 17.
10 Not to be turned in 13.7)3, 9, 17, 29, 35, 37;
13.8)3, 5, 9, 13, 17, 23, 33, 35, 37.

Tests and exams
There will be a midterm on Monday May 3. The final exam will be on Monday, Jun 7, 12-3pm.

Grading
The final grade is based on quizzes, 10%, homeworks, 15%, midterm, 25%, and the final exam, 50%.

A Few Words to the Student
Come to the lecture and sections prepared. Keep up with the reading schedule, and start working on each assignment well in advance of the due date. A single problem may take hours to solve. Only you can convince yourself how clear a solution can be. And as much as your Professor and the TA's are commited to helping you along, you also have to work hard to make that possible.