Please make sure to write clearly and that the assignment number and your name appear at the top of the first page. After that, we will for the most part proceed linearly through the textbook at a steady rate. Read as necessary, depending on your knowledge of topology. Cambridge University Press, Any sections to be skipped or material to be covered out of order will be announced in advance.

Problems are listed using notation like Sec 1. Harmonic functions, Poisson kernel. I will assume the material in the first chapter on the algebraic properties of complex numbers and their geometric representation. Monday classes — no meeting. Grading Your course grade will be determined on the following basis: The inversion of the UIC circle mark in its boundary.

Linear Fractional transformations, elementary mappings.

# Complex Variables

oslutions Monday classes — no meeting. Final Exam in class. Homework 7 due Monday, Feb 29 — Geometric properties of holomorphic functions Sec 4. The date for the final exam will be announced on this page well in advance.

Any sections to be skipped soputions material to be covered out of order will be announced in advance. Problems are listed using notation like Sec 1.

Late homework is not accepted. There will be a total of eight problems on the exam, and you will be asked to complete any five of them.

## Complex Analysis I

The mailroom is located on the 3 rd floor of SEO. The exponential and logarithmic functions. I will assume the material in the first chapter on the algebraic properties of complex numbers and their geometric representation.

Chapter 2, sec 1. Complex Analysis by L. There are countless online tutorials, references, and resources, but these simple templates might help you get started: Chapter 3 sections 3, 4 selected problems 3. Course meetings, Tues -Thurs The sections under discussion will be announced in each lecture, and it is up to you to keep up with the corresponding reading.

Schwarz reflection principle, zeros, poles and residues, Calculus of residues, applications to definite integrals. Course Outline – Mat – Fall The final grade will be based on the midterm and final exam and the homework grades. Important Dates There will be one midterm exam and a cumulative final exam.

The final will be in class on Dec Please make sure to write clearly and analysjs the assignment number and your name appear at the top of the first page.

Grading Your course grade will be determined on the following basis: Families of Analytic Functions. About the final exam The final exam will take place on Friday May 6, Reading By the end of the first week, read chapter 1 and the first two sections from chapter 2. Students are strongly advised to work on all the homework problems to make sure they are keeping pace with the class. No Class Rosh Hashana.

Harmonic functions, Poisson kernel. That is, after discussing the gamma function we will move on to normal families 5.

Gamelin Bak and Newman. Outline I plan to give a very standard beginning complex analysis course. Contents of the homrwork By appointment Outline I plan to give a very standard beginning complex analysis course. Poisson Integral, Schwarz reflection Chapter 4.