SYLLABUS

Vector Analysis (Math 550, Section 1)
Spring 2002, USC

Lecture
M W F 12:20-1:10 LC 401A
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
A grade of C or better in Math 241--familiarity with basics of vector algebra (dot products and cross products), partial derivatives, gradients, and multiple integrals.

Textbook
Vector Calculus, by Susan Colley, second edition.

Homeworks
There will be homework assignments due every Wednesday. Late homeworks will not be accepted.

Lecture and Reading Schedule
Dates Lectures
Jan 14
16
18		 M
W
F		 1.1
1.2
1.3		 Intro to vectors
Intro to vectors
Dot products
21
23
25		 M
W
F		 .
1.4
1.4		 MLK day
Cross Products
Cross Products
28
30		 M
W		 1.5
1.5		 Equations for planes
Distance problems
Feb 1 F 1.5 Distance problems
4
6
8		 M
W
F		 3.1
3.1
3.1		 Parametrized curves
Parametrized curves
Kepler's and Newton's Laws
11
13
15		 M
W
F		 3.3
3.4
.		 Vector fields
Divergence and Curl
Midterm 1
18
20
22		 M
W
F		 3.2
3.2
5.1		 Arc Length
Arc Length
Cavalieri's Principle
25
27		 M
W		 5.2
5.2		 Double integrals
Double integrals
Mar 1 F 5.3 Changing the order of int.
4
6
8		 M
W
F		 5.4
5.4
5.5		 Triple Integrals
Triple Integrals
Change of Variables
Mar 11
13
15		 M
W
F		 .
.
.		 Spring Break
Spring Break
Spring Break
18
20
22		 M
W
F		 5.6
5.6
6.1		 Applications of integrals
Applications of integrals
Scalar and Vector Line integrals
25
27
29		 M
W
F		 6.1
.
.		 Scalar and Vector Line integrals
Review
Midterm 2
Apr 1
3
5		 M
W
F		 .
6.2
6.2		 Easter
Green's theorem
Green's theorem
8
10
12		 M
W
F		 6.3
6.3
7.1		 Conservative vector fields
Conserative vector fields
Parametrized surfaces
15
17
19		 M
W
F		 7.1
7.2
7.2		 Parametrized surfaces
Surface integrals
Surface integrals
22
24
26		 M
W
F		 7.3
7.3
7.3		 Stokes's and Gauss's Theorems
Stokes's and Gauss's Theorems
Stokes's and Gauss's Theorems
29 M 7.4 Maxwell's equations
May 1 W . Review
7 Tu . Final Exam (Comprehensive)

Assignments
# Due Date Problems
1 Jan 23 1.2) 6--10, 13--18, 24, 25, 28,
1.3) 4, 6, 8, 9, 10, 11, 12, 14, 15, 16, 24, 25, 26.
2 Jan 30 1.3) 21;
1.4) 3, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 31;
1.8) 18a, 19a, 20.
3 Feb 6 1.5) 1, 2, 3, 4, 5, 6, 7, 20, 21, 22, 23, 24, 25, 27, 28, 29;
1.8) 12, 15.
4 Feb 13 3.1) 3, 7, 8, 15, 16, 17, 20, 21, 22, 25, 26, 27, 28.
5 Feb 20 3.3) 1, 2, 3, 23;
3.4) 2, 3, 8, 14, 15, 16, 18, 23.
6 Feb 27 3.2) 1, 2, 3, 7, 8, 9, 10, 12;
5.1) 1, 2, 3, 4, 7, 10, 11.
7 Mar 6 5.2) 1, 2, 3, 4, 5, 12, 13, 15, 20, 21, 23, 26;
5.3) 1, 2, 5, 6, 8, 9, 11, 12, 14.
8 Mar 20 5.4) 1, 2, 5, 6, 8, 11, 14, 15;
5.5) 9, 13, 14, 15, 16, 21, 23, 24, 25, 28;
5.7) 19.
9 Mar 27 5.6) 3, 9, 14, 18;
5.7) 11, 12, 16a.
10 Apr 3 6.1) 1, 2, 6, 7, 11, 12, 16, 20, 21.
11 Apr 10 6.2) 1, 2, 5, 8, 10, 12, 13, 16, 17.
12 Apr 17 6.3) 1, 2, 3, 4, 7, 8, 14, 15, 19;
6.4) 1, 4, 22.
13 Apr 24 7.1) 1, 8, 10, 16, 18, 20;
7.2) 1, 7, 8, 9, 12, 13, 17, 18;
7.5) 4, 7.
14 May 1 7.3) 1, 2, 6, 7, 10, 11, 12, 15, 18, 20, 23.

Tests and Exams
There will be 2 midterms on Fridays Feb 15 and Mar 29. The Final Exam is on Tuesday, May 7 , 2-5 pm.

Grading
Your final grade is comprised of the homeworks (20%), midterms (20% each) and the final exam (40%).

Attendance Policy
Consistent with the USC undergraduate bulletin a grade penalty may be applied to any student missing more than 3 lectures during the semester.