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

Math 4317 and Math 4320 or equivalent

Location and Schedule:
Skiles  240,   Tuesday-Thursday 12:05-1:25PM

Final Exam
Thursday May 1st 8-
Skiles 240

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

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)