# Math 5021: Complex Analysis I

## FALL 2017

Welcome to the webpage for Math 5021. This is an introductory graduate level course on complex analysis.

The course will include topics on holomorphic functions, conformal mappings, Cauchy's Theorem and consequences, Taylor and Laurent series, singularities, residues, and other topics as time permits.

Math 5021-5022 form the basis for the Ph.D. qualifying exam in complex variables.

** Time/Location **
Tu-Th 1-2:30PM, Cupples I, Room 111

** Prerequisites: **
Math 4111, 4171 and 4181, or permission of the instructor.

** Textbook: **
There is no required textbook for the course. I will be following Complex Analysis by Ahlfors (3rd edition) closely. Additional useful books are:

Complex Analysis by Stein and Shakarchi

Functions of one complex variable by Conway

Function theory of one complex variable by Greene and Krantz

A copy of each of these books is placed on reserve at Olin Library.

** Office hour: **
Tuesday 2:30-3:30, Wednesday 4-5, or By appointment. Location: Cupples I, Room 108B.

**Grader: **
The grader for this course is Wei Wang (wang.w@wustl.edu).

**Exams: **
There will be one in class midterm exam during the semester. There will also be a final exam.
The midterm is tentatively scheduled for Tuesday October 24. If you are unable to take the midterm exam for legitimate reasons, you will not be given a make up exam.

The solutions to the midterm exam can be found here.

** Grading Information: **
The midterm and the homework will each count for 30 percent of your grade. The final exam will count for 40 percent of your grade.

** Homework: **
There will be weekly homework. The homework is due on Tuesdays (starting from September 7) at the beginning of class. Late homework
will not be accepted.

You are encouraged to discuss the problems but the write-up must be your own.

I expect there will be 12 (or 11) problem
sets. The lowest homework grade will be dropped and the remaining 11 (or 10) will be counted towards your final course grade.

1. Homework #1 , Due September 12, in class. Solutions

2. Homework #2 , Due September 19, in class. Solutions

3. Homework #3 , Due September 26, in class. Solutions

4. Homework #4 , Due October 3, in class. Solutions

5. Homework #5 , Due October 12, in class. Solutions

6. Homework #6 , Due October 19, in class. Solutions

7. Homework #7 , Due November 9, in class. Solutions

8. Homework #8 , Due November 17, in class. Solutions

9. Homework #9 , Due November 28, in class. Solutions

10. Homework #10 , Due November 7, in class. Solutions