SYLLABUS

Vector Analysis (Math 550, Section 1)
Fall 2001, USC

Lecture
M W F 10:10-11:20 LC 401
Instructor
Professor Mohammad Ghomi Check the course web site periodically to obtain revised versions of this syllabus, homework assignments, and copies of old tests.

Course Description
We study calculus of vector valued functions. Main topics include parametrized curves and surfaces, change of variables formula and Jacobians, line and path integrals, surface integrals, theorems of Green, Gauss, Stokes, and various applications to problems in Physics, Engineering, and Geometry.

Prerequisites
Math 241--familiarity with basics of vector algebra (dot products and cross products), partial derivatives, gradients, and multiple integrals.

Textbook
Vector Calculus, by Jerrold E. Marsden and Anthony J. Tromba, fourth edition.

Homework and Quizzes
There will be homework assignments due every Wednesday. Late homeworks will not be accepted.

Lecture and Reading Schedule
Dates Lectures
Aug 24 F 1.1 Intro. to vector geometry
27
29
31		 M
W
F		 1.2
1.2,1.3
1.3		 Dot products, length
Practice Quiz 1
Cross products
Sep 3
5
7		 M
W
F		 .
.
2.4, 4.1		 Labor Day-no classes
Practice Quiz 2
Intro to space curves
10
12
14		 M
W
F		 4.1
.
.		 Parametrizations
Review
Exam 1
17
19
21		 M
W
F		 4.1
4.2
4.3		 Velocity and acceleration
Arc-length, Practice Quiz 3
Vector fields
24
26
28		 M
W
F		 4.3
.
4.3		 Vector Fields
Practice Quiz 4
Vector Fields
Oct 1
3
5		 M
W
F		 4.4
4.4
5.1		 Curl and Divergence
Curl and Divergence
Intro. to Volumes, Cavalieri's principle
8
10
12		 M
W
F		 5.2
5.3
.		 Double integrals over rectangles
Double integrals over general domains
Exam 2
15
17
19		 M
W
F		 .
5.6
1.4		 Fall Break-no classes
Triple Integrals
Spherical and Cylindrical Coordinates
Oct 22
24
26		 M
W
F		 6.1,6.2
6.3
6.3		 Change of Variables in Integrals
Applications
Applications
29
31		 M
W		 7.1
7.2		 Path Integrals
Line Integrals
Nov 2 F 7.2,7.3 Line Integrals, Parametrized Surfaces
5
7
9		 M
W
F		 7.3
7.4
.		 Parametrized Surfaces
Area of Surfaces
Exam 3
12
14
16		 M
W
F		 7.5
7.6
8.1		 Integral of scalars on surfaces
Inegral of vectors on surfaces
Green's Theorem
19
21
23		 M
W
F		 8.2
.
.		 Stokes Theorem
Thanksgiving-no classes
Thanksgiving-no classes
26
28
30		 M
W
F		 8.3
8.4
8.4		 Conservative Fields
Gauss' Theorem
Gauss' Theorem
Dec 3
5
7		 M
W
F		 8.5
8.5
.		 Applications
Applications
Review
14 F . Final Exam
.

.

Assignments
Homework # Due Date Problems
1 Aug 29 1.1) 6, 8, 11, 13, 16, 17, 23, 24, 26.
2 Sep 5 1.2) 2, 14, 17, 19, 22;
Practice Quiz 1.
1.3) 4, 6, 16.
3 Sep 12 1.3) 17, 20, 24, 31;
First 4 problems in Practice Quiz 2.
4 Sep 19 2.4) 2, 10, 14, 16, 18;
4.1) 6, 14, 18, 20, 21.
5 Sep 26 4.2) 1, 10, 11, 12, 13;
All problems in Practice Quiz 3.
6 Oct 3 4.3) 2, 4, 8, 11, 15, 17;
All problems in Practice Quiz 4.
7 Oct 10 4.4) 10, 13, 26, 30;
p. 290) 7, 8.
8 Oct 17 5.1) 3, 4, 5, 6;
5.2) 1c, 2c, 5, 6;
5.3) 1c, 2a, 3, 8, 11, 12.
9 Oct 24 5.6) 4, 5, 10, 19;
1.4) 1b, 4, 9.
10 Oct 31 6.2) 1, 3a, 9, 13, 21, 29;
6.3) 2, 4, 9, 10;
6.4) 12;
p.394) 21.
11 Nov 7 7.1) 2c, 3b, 9, 11, 12;
7.2) 1b, 2a, 3, 4, 10, 14, 17.
12 Nov 14 7.3) 2, 5, 11, 12;
7.4) 3, 4, 6, 7, 11, 14, 16.
13 Nov 19 7.5) 2, 4, 9, 10, 11;
14 Nov 28 7.6) 2, 3, 4, 15, 16;
8.1) 2, 3a, 4, 12, 13, 20.
15 Dec 5 8.2) 2, 3, 7, 8, 17, 19;
8.3) 1, 4, 5, 6, 7, 12.

Tests and Exams
There will be 3 midterms on Fridays Sep 14, Oct 12, and Nov 9. The Final Exam is on Friday, December 14 , 9-12 am.

Grading
Your final grade is comprised of the homeworks (15%), midterms (15% each) and the final exam (40%).

Study Hints and Guidelines
Solving Calculus problems, much like playing a musical instrument, is a skill, which can be developed only through persistent practice. Plan to work on the homework assignments everyday, and for a total of at least 10 hours each week.

Also, it is very important that you attend all lectures. Consistent with the USC Undergraduate Bulletin, a grade penalty may be applied to any student missing more than three classes during the semester.

You are strongly encouraged to ask questions during the lectures, and participate in classroom discussions. Further, feel free to see your instructor during the office hours. If you cannot come at the scheduled hours, you may knock on the Professor's door at any other time, or send an email for an appointment.