COMPLEX ANALYSIS
Math
2101, Spring 2010
Instructor: Dr. Rachel Hall
Office: 229
Barbelin
Office
Hours: M 2:30-4, W 2-3:30, F 1-2 and by appointment
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 or
consent of instructor
Text: Complex Variables
and Applications,
James Ward Brown and Ruel V. Churchill, seventh edition. McGraw Hill,
2003.
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 two
midterms and a final. 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 final will be cumulative.
Grades: Grades will be
assigned on the following basis:
3% class
participation
7% function
diary project (includes presentation and paper)
25% homework (lowest grade
dropped)
40% two midterms
25% final (may replace your
lowest midterm grade, if it is lower than your grade on the final)
The grade
cutoffs are 90% A, 86.7% A-, 83.3% B+, 80% B, 76.6% B-, 73.3% C+, 70% C, 65%
C-, 60% D+, 55% D, and below 55% F.
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 2009-2010.
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 |