COMPLEX ANALYSIS
Math 2101, Spring 2006
Instructor: Dr. Rachel Hall
Office: 229 Barbelin
Office Hours: M 11-12, T 2-3, R 3:45-4:45
Telephone: (610) 660-3096 (Office)
E-mail: rhall@sju.edu
URL: http://www.sju.edu/~rhall/Complex
Course Description: Complex
analysis, the theory of functions of complex numbers, is one of the crowning
achievements of nineteenth century mathematics. Although complex numbers are sometimes called imaginary
numbers, complex analysis is far from imaginary; it has a multitude
of real-world applications to engineering, physics, and applied
mathematics. We will cover
Chapters 1-4 in the textbook, plus selected topics in Chapters 5, 6, and
8. Topics include properties of complex numbers, analytic functions,
mapping, contour integrals, the fundamental theorem of algebra, and Cauchy’s
residue theorem. I will pay
special attention to the geometric properties of complex functions.
Prerequisite: Real Analysis
Text: Complex Variables and
Applications, James Ward Brown and Ruel V. Churchill, seventh
edition. McGraw Hill, 2003.
Computer Software: f(z),
Windows software for visualizing complex analysis.
Homework: Homework assignments
will be posted at http://www.sju.edu/~rhall/Complex/homework.html.
There will be about ten homework assignments; the lowest grade will be
dropped. You should start working on the homework problems for a section
as soon as that section is covered in class. Although you are encouraged
to consult with other students and seek help from me, your homework should
ultimately represent your own work. For more information, see the
department’s Academic Honesty guidelines. Answers unsupported by work will
not receive credit. Homework should be neatly handwritten or typed, on
one side of the page only. Please
remove messy edges and staple.
Function diary: Each of
you will be assigned a function at the beginning of the semester. You will
be asked to keep a diary of how each new topic applies to your function.
You will also be asked to present examples relating to your function in
class. The project will culminate in a paper.
Tests: There will be three
tests. The first two will be given in class. The third will be given during
finals week. Makeup tests will only be given to students who contact
me within 48 hours of missing a test.
Students with a valid, verifiable reason for missing a test may take a makeup
without penalty; those who have missed a test without a valid, verifiable
reason may take a makeup with a 30% penalty. The tests will not be
cumulative.
Grades: Grades will be
assigned on the following basis:
10% function diary
25% homework (lowest grade dropped)
65% three midterms
The grade cutoffs are 94% A, 90% A-, 87% B+, 84% B, 80% B-, 77% C+, 74% C,
70% C-, 67% D+, 60% D, and below 60% F. Grades may be curved at the end of the
semester.
Academic Honesty: Dishonesty
includes cheating on a test, falsifying data, misrepresenting the work of
others as your own (plagiarism), and helping another student cheat or
plagiarize. Academic dishonesty will result in a grade of zero on that
particular assignment; serious or repeated infractions of the Academic Honesty
policy will result in failure of the course. All violations of the Academic
Honesty policy will result in the filing of a violation report. For complete information about the
University's policy on Academic Honesty, consult the
department’s Academic Honesty guidelines and the Student Handbook
2005-2006.
Attendance: If you do miss a
class, it is your responsibility to make up the material and make sure your
homework is turned in on time.
Schedule:
|
Weeks |
Topics |
|
2 |
Chapter 1 |
|
3 |
Chapter 2 |
|
2 |
Chapter 3 |
|
1 |
Chapter 8 |
|
2 |
Chapter 4 |
|
1 |
Chapter 5 |
|
1 |
Chapter 6 |