Outline:

1. Cauchy's Theorem and Its Applications
2. Meromorphic Functions and the Logarithm
3. Conformal Mappings
4. Entire Functions
5. Gamma and Zeta Functions and Applications

Objective:

This is supposed to be a second course on complex variables. After a quick review of the Cauchy Theorem and Residue Theorem, we shall study the conformal mapping and entire functions in detail. Then we shall apply those theories to understand complex functions such as gamma function, zeta function.

Textbook:

1. E.M. Stein and R. Shakarchi, Complex Analysis
2. J.B. Conway, Functions of One Complex Variable, 2nd ed.