SYLLABUS

Vector Calculus (Math 241, Section 1)
Fall 2000, USC

Lecture
M W F 9:05-9:55 am LC 405.
Instructor
Professor Mohammad Ghomi
Check the course web site periodically for revised versions of this syllabus, and to obtain homework assignments and copies of old tests and quizzes.

Course Description
We will study derivatives and integrals of functions of several variables with a view towards studying geometry of curves and surfaces in 3-space, together with a host of other applications in Physics and Engineering.

Prerequisites
Math 142--a sound understanding of derivatives and integrals of functions of one variable.

Textbook
Calculus, by J. Varberg, Pursell, and Rigdon, Seventh Edition.

Homework and Quizzes
There will be weekly homework assignments due each week. Late homeworks will not be accepted.

Also, there will be some practice quizzes. You should save copies of these quizzes as they are a very good source for preparing for the final and midterms.

Doing the homework problems is the most important part of this class. You may work with a group of your classmates if you are all at about the same level; however, you should definitely try to do many problems on your own. Further, try to practice doing at least some of the problems in settings which resemble that of the test and quizzes, i.e., without using your calculator or constantly referring to the textbook.

Lecture and Reading Schedule
You should make a sincere effort to keep up with your reading assignments; otherwise, you may significantly compromise your ability to benefit from the lectures.
Dates Lectures
Aug 25 F 13.1 Parametric curves in the plane
28
30		 M
W		 13.2
13.3		 Vectors in the plane
Vectors in the plane
Sep 1 F 13.4 Vector Functions
4
6
8		 M
W
F		 .
13.5
14.1		 Labor day-no classes
Curvature and Acceleration
Coordinates in 3-Space
11
13
15		 M
W
F		 14.2
14.2, 14.3
14.3		 Vectors in 3-Space
Dot Product
Cross Product
18
20
22		 M
W
F		 14.4
.
.		 Lines and Curves in 3-Space
Review
Midterm 1(covers up to and including 14.2)
25
27
29		 M
W
F		 14.5
14.6
14.7		 Velocity and Acceleration
Surfaces in Three-Space
Cylindrical and Spherical Coordinates
Oct 2
5
7		 M
W
F		 15.1
15.1, 15.2
15.2		 Functions of several variables
Graphs
Partial Derivatives
9
11
13		 M
W
F		 15.4
15.5
15.6		 Gradients
Directional Derivatives
The Chain Rule
16
18
20		 M
W
F		 .
.
.		 Fall Break-no classes
Review
Midterm 2(covers up to and including 15.5)
23
25
27		 M
W
F		 15.7
15.8
15.9		 Tangent Planes and Approximations
Maxima and Minima
Lagrange's Method
30 M 16.1 Double Integrals over Rectangles
Nov 1
4		 W
F		 16.2
16.3		 Iterated Integrals
Double Integrals over Nonrectangular Regions
6
8
10		 M
W
F		 16.3
16.4
16.5		 More Double Integrals
Double Integrals in Polar Coordinates
Applications of Double Integrals
13
15
17		 M
W
F		 16.5
.
.		 Applications of Double Integrals
Review
Midterm 3 (covers up to and including 16.4)
20
22
24		 M
W
F		 16.7
.
.		 Triple Integrals (rectangular coordinates)
Thanksgiving Recess-no classes
Thanksgiving Recess-no classes
27
29		 M
W		 16.7
16.8		 Triple Integrals (rectangular coordinates)
Triple Integrals (spherical and cylindrical coordinates)
Dec 1 F 16.8 Triple Integrals (spherical and cylindrical coordinates)
4
6
8		 M
W
F		 .
.
.		 Applications of Triple Integrals
Review
Review
13 W . Final Exam(Comprehensive)

Assignments
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 Sep 4 13.1)2, 8, 17, 26, 44, 57;
13.2) 2, 4, 6, 14;
13.3) 2, 4, 10, 12, 14, 16, 26, 30.
2 Sep 11 13.4)14(a), 18, 24, 32, 36, 38;
13.5) 2, 13, 29.
3 Sep 18 14.1) 7, 11(a), 12, 14, 25, 29;
14.2) 6, 8, 12, 13, 23, 25(a), 28;
4 Sep 25 14.3) 4, 6, 10, 12, 18, 26;
14.4) 2, 6, 14, 24, 28, 29.
5 Oct 2 14.5) 7, 14, 15, 40, 58;
14.6) 2, 9, 10, 16, 21.
6 Oct 9 14.7) 2, 3, 4, 8, 17, 18, 30;
15.1) 2, 8, 14, 18, 23.
7 Oct 16 15.2)4, 18, 30, 33;
15.4)2, 6, 12;
15.5)4, 10, 16, 18, 20, 23.
8 Oct 23 15.6) 2, 14, 17, 18, 20.
9 Oct 30 15.7) 2, 14, 22, 23;
15.8) 2, 5, 12, 14, 16, 18, 19.
10 Nov 6 15.9) 2, 7, 8, 10;
16.1) 2, 6, 10, 15;
16.2) 6, 8, 14, 20.
11 Nov 13 16.3) 2, 10, 14, 24, 38, 39;
16.4) 4, 5, 11, 14.
12 Nov 27 16.5) 2, 5, 6, 8;
16.7) 2,4, 16, 19, 20, 22.
13 Dec 4 16.8) 1, 2, 5, 7, 12, 17, 22, 23.

Tests and Exams
There will be three midterms on Fridays Sep 22, Oct 20, and Nov 17. The final exam will be on Wednesday, Dec 13, 9 am. No calculators, or notes will be allowed during the exams. Note: bring a bluebook to the exams.

Grading
The final grade is based on homeworks and quizzes, 15%, midterms, 15% each, and the final exam, 40%.

A Few More Study Hints and Guidelines
Learning Mathematics is a demanding affair. It requires a good deal of self discipline and hard work to appreciate the power and beauty of the subject. Further, solving Calculus problems, much like playing a musical instrument, is a skill, which can be developed only through persistent practice. You should plan to work on your exercises everyday, and for a total of at least 10 hours each week. Also, it is very important that you faithfully attend all lectures.

A good deal of class time shall be devoted to working through problems. Do not get into the habit of sitting passively and expect the professor to make you understand. Rather, you should take out your paper and pencil and try to do the problems at the same time with your instructor. If something is unclear to you, feel free to ask questions, and if you need more help, go see your instructor and/or the TA during the office hours. If you cannot come during the office hours, you are welcome to knock on the professor's door at another time, or send an email for an appointment.

Calculus is one of the greatest accomplishments of the human mind. Having the opportunity to study it is a true privilege, and an excellent chance to practice the art of thinking in a clear and organized way. I hope that this class will be a rewarding experience for you.