Textbook
Complex Analysis by E. Stein and R. Shakarchi
Other good books are: Ahlfors's Complex Analysis, and
Conway's Functions of one complex variable.
Grading
Your grade will be based on several homework assignments
(30%), one Midterm (30%) and a Final exam (40%). The
exams will most likely be in class.
Office Hours
I'll be available from 2-4:00 on Monday afternoons.
You can also email me and schedule an appointment.
The CA for our course is Ian Petrow. His
office is in 381-B, and he will hold office hours on Wednesdays 1-3.
Midterm
The midterm will be on Tuesday November 1. It'll be inclass,
and closed book/notes.
It will cover Chapters 1-3, 5, and Appendix B of the book plus other
material discussed in class (e.g. the homology form of Cauchy's theorem,
and the general discussion of holomorphic functions with prescribed
zeros etc).
Midterm and Solutions.
Final
The final exam will be on Wednesday, December 14 from 7 to 10 PM.
Homework Assignments
Homework will be assigned every Tuesday, and due the
following Tuesday. I will not accept late assignments. I know everyone is
likely to have an off-week, and I will drop your lowest
score.
Homework 1: Due Tuesday October 11. Do ten from the following problems.
Chapter 1: Exercises 6, 7, 9, 10, 11, 16(d,e,f).
Chapter 2: Read Section 2.3. Exercises 2, 5, 7, 8, 13.
Chapter 2. Problems 1(a), 2. (These two problems are required
for Math grad students).
Solutions due to Emil Baronov.
Homework 2: Due Tuesday October 18.
Chapter 3: Exercises 1, 14, 15, 16, 17. Also read Section 3.2.1, and
do either (a) five of exercises 2-12 from Chapter 3, or (b) three
of exercises 2-12 from Chapter 3 and Problem 3 from Chapter 3.
Math grad students must do option (b).
Solutions due to Emil Baronov.
Homework 3: Due Tuesday, October 25. Chapter 2: Exercise 10,
Problem 4. Chapter 3: Exercises 18, 21, 22. Chapter 5: Exercises 3,5,
and Problem 1.
Additional Problem: Consider the region R obtained
by removing the interval [-1,1] from the complex plane. Prove that
on R one can define a holomorphic function log ((z+1)/(z-1)). Prove
that one can define a holomorphic function \sqrt(1-z^2) on this region.
Let gamma denote a cycle in R. What are the possible values of
the integral around gamma of 1/\sqrt{1-z^2}?
Solutions due to Emil Baronov.
Homework 4: Due Tuesday November 1. Chapter 5: Exercises 1, 6, 7,
10, 11, 13, 17 (In part b, there is a typo and the first term
in the definition of F should have E'(0) in the denominator.)
Chapter 5: Problems 3 and 4. For Problem 3 you may find Stirling's
formula helpful, and may assume any useful version of it.
Solutions due to Emil Baronov.
Homework 5: Due Tuesday, November 8. Chapter 6: Exercises 1, 3, 5,
7, 10, 12, 15, 17. Chapter 6: Problems 2 and 3.
Solutions due to Emil Baronov.
Homework 6: Due Tuesday, November 15. Chapter 6: Exercise 16.
Problem 1 (there's a typo in part a, and it should be N^{1-s} instead of
N^{s-1}). Chapter 7: Exercises 1, 2, 3, 5, 6, 7 (read Schwarz's reflection
principle Chapter 2, section 5.6), 8.
Homework 7: Due Tuesday, November 29. Chapter 8: Exercises 3, 4, 10, 11, 12, 13, 15. Problems 2 and 5.
Homework 8: Due Tuesday, December 6. Chapter 8: Exercises, 20, 24 a,b.
Problem 9. Chapter 9. Exercises 1, 2, 4, 5. Problem 4.