6321-Complex Analysis
(Spring 2008)
Jean
Bellissard
CRN 21189 MATH6321
Professor
of Mathematics and
Physics
School
of Mathematics, Skiles
132
Phone: (404)
385-2179
Fax: (404)
894-4409
e-mail: jeanbel@math.gatech.edu
Prerequisites:
Math
4317 and Math
4320 or equivalent
Location and Schedule:
Skiles 240, Tuesday-Thursday 12:05-1:25PM
|
Final Exam: May 1st, 2008, 8-10:50, Skiles 240
The final exam will consist of questions taken from, or inspired by, the
exercises found in the textbook John B. Conway, Functions of one complex
variable, Vol. I, 2nd edition,
Springer (last printing: 2005). These
questions will cover all chapters taught in class including the ones
taught during the last week of course.
The questions will emphasize upon practical calculations and use of main
theorems to justify them rather than on mathematical proofs of
fundamental
results.
Course description
Analytic
functions
Series and
integration theorems and formulas; Goursat's theorem
Singularities,
the argument principle, Rouche's theorem
Conformal
mapping by elementary functions
Harmonic
families and Poisson's formula
The maximum
principle and Schwarz's lemma
Spaces of
analytic functions and normal families
The Riemann
mapping theorem and the Weierstrass factorization theorem
Analytic
continuation, multi-valued analytic functions, and Riemann surfaces
Additional
topics as time permits and interest dictates, e.g., the theorems of
Runge,
Picard, and Mittag-Leffler, Bergman's kernel, moment problems,
elliptic functions,
zeros of analytic functions, the Schwarz-Christoffel transformation
Main Textbook
John B. Conway, Functions
of one complex variable,
Vol. I, 2nd edition,
Springer (last printing: 2005)
Another useful
textbook
John B. Conway, Functions of one complex variable,
Vol. II,
Springer (1995)
Elias M. Stein, Rami Shakarchi
Complex Analysis
(Princeton Lectures in Analysis Series Vol. II)
Princeton University Press (2003)