That is, after discussing the gamma function we will move on to normal families 5. There will be a total of eight problems on the exam, and you will be asked to complete any five of them. No lectures about section 3. The final will be in class on Dec Read as necessary, depending on your knowledge of topology. I will assume the material in the first chapter on the algebraic properties of complex numbers and their geometric representation.

Complex Analysis by Lars Ahlfors, 3ed. Chapter 3 sections 3, 4 selected problems 3. The exponential and logarithmic functions. Any sections to be skipped or material to be covered out of order will be announced in advance. By appointment Outline I plan to give a very standard beginning complex analysis course. Complex numbers, holomorphic functions, Cauchy-Riemann equations, power series, complex integration. Normal Families Equicontinuity and Compactness.

Homework is accepted until the solutions have been posted. The exponential and logarithmic functions. Homework 7 due Monday, Feb 29 — Geometric properties of holomorphic functions Sec 4. Read as necessary, depending on your knowledge of topology. Problems are listed using notation like Sec 1. I expect to cover the material in Ahlfors in the first semester.

Polynomial and Rational Functions.

## CHEAT SHEET

The date for the final exam will homfwork announced on this page well in advance. Power Series and Exponential Functions. The sections under discussion will be announced in each lecture, and it is up to you to keep up with the corresponding reading.

Other classical texts you may want to consult are: Normal Families Equicontinuity and Compactness.

# Complex Analysis

Any sections to be skipped or material to be covered out of order will be announced in advance. Poisson Integral, Schwarz reflection Chapter 4.

That is, each challenge problem is worth as much as a weekly homework assignment! Some of the material can also be found in Hyperbolic Geometry from a local viewpoint, L.

Complete problems 3 and 5 on this list. Gamelin Bak and Newman.

Weekly homework Suggested exercises — Elliptic Functions Sec 7. Unless otherwise noted, all problems refer to the main textbook, Complex Analysis3 rd Edition, by Lars Ahlfors.

Students are strongly advised ahlforz work on all the homework problems to make sure they are keeping pace with the class. Reading By the end of the first week, read chapter 1 and the first two sections from chapter 2. The final grade will be based on the midterm and final exam and the homework grades.

Homework assignments will appear on this page approximately every week. Chapter 3 sections 3, 4 selected problems 3. About the final exam The final exam will take place on Friday May 6, There are countless online tutorials, references, and resources, but these simple templates might help you get started: The mailroom is located on the 3 rd floor of SEO.

# Complex Variables

Grading Your course grade will be determined on the following basis: Course meetings, Tues -Thurs Families of Analytic Functions. Staple your homework if it spans several sheets of paper. That is, after discussing the gamma function we will move on to normal families 5. Exponential and Trigonometric functions. Ajlfors lectures about section 3.