# COMPLEX ANALYSIS COURSE TEXT AHLFORS HOMEWORK SOLUTIONS

Exponential and Trigonometric functions. Power Series and Exponential Functions. Unless otherwise noted, all problems refer to the main textbook, Complex Analysis , 3 rd Edition, by Lars Ahlfors. That is, after discussing the gamma function we will move on to normal families 5. Complete problems 3 and 5 on this list. Complex numbers, holomorphic functions, Cauchy-Riemann equations, power series, complex integration. The final grade will be based on the midterm and final exam and the homework grades.

Complex numbers, holomorphic functions, Cauchy-Riemann equations, power series, complex integration. Homework 12 due Monday, Apr 11 — Products Sec 5. The exponential and logarithmic functions. The final will be in class on Dec That is, after discussing the gamma function we will move on to normal families 5.

Read Chapter 1 and Chapter 2 sec 1ex: Normal Families Equicontinuity and Compactness. Course meetings, Tues -Thurs Typeset solutions are welcome, but not required. Families of Analytic Functions.

About the final exam The final exam will take place on Friday May 6, The compplex for the final exam will be announced on this page well in advance.

GRADUATION SPEECH OF TIFFANY GRACE UY

The mailroom is located on the 3 rd floor of SEO. The final grade will be based on the midterm and final exam and the homework grades.

## Complex Analysis I

Reading By the end of the first week, read chapter 1 and the first two sections from chapter 2. I expect to cover the material in Ahlfors in the first semester. Poisson Integral, Schwarz reflection Chapter 4. Unless otherwise coyrse, all problems refer to the main textbook, Complex Analysis3 rd Edition, by Lars Ahlfors.

# Complex Variables

The suggested reading for the material for this is: No lectures about section 3. Chapter 2, sec 1.

Power Series and Exponential Functions. There will be a total of eight problems on the exam, and you will be asked to complete any five of them. Homework 12 due Monday, Apr 11 — Products Sec 5. Complex Analysis by L.

Schwarz reflection principle, zeros, poles and residues, Calculus of residues, applications to definite integrals. That is, after discussing the gamma function we will move on to normal families 5.

Grading Your course grade will be determined on the following basis: Quick review of elementary point set topology. After that, we will for the most part proceed linearly through the textbook at a steady rate.

PROBLEM SOLVING BOARD HISD

Students are strongly advised to work on all the homework problems to make sure they are keeping pace with the class. Monday classes — no aalysis. Cambridge University Press, Other classical texts you may want to consult are: Please make sure to write clearly and that the assignment number and your name appear at the top of the first page.

Final Exam in class. Homework is accepted until the solutions have been posted.

## CHEAT SHEET

Complete problems 3 and 5 on this list. Late homework is not accepted. Harmonic functions, Poisson kernel.

Contents of the course: