*Prerequisites:*

Math
4317 and Math
4320 or equivalent

*Location and Schedule:*

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

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.

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

* *

Springer (last printing: 2005)

Another useful
textbook

John B. Conway, Functions of one complex variable,
Vol. II,

Springer (1995)

Complex Analysis (Princeton Lectures in Analysis Series Vol. II)

Princeton University Press (2003)