After that, we will for the most part proceed linearly through the textbook at a steady rate. There are countless online tutorials, references, and resources, but these simple templates might help you get started: Final Exam in class. Families of Analytic Functions. By appointment Outline I plan to give a very standard beginning complex analysis course. No lectures about section 3.

The exponential and logarithmic functions. Poisson Integral, Schwarz reflection. Poisson Integral, Schwarz reflection Chapter 4. Staple your homework if it spans several sheets of paper. Cambridge University Press, Homework assignments will appear on this page approximately every week.

The inversion of the UIC circle mark in its boundary. The exponential and logarithmic functions.

# Complex Analysis

Outline I plan to give a very standard beginning complex analysis course. Staple your homework if it spans several sheets of paper. Complex Analysis by L. Homework is accepted until the solutions have been posted.

## Complex Analysis I

Read Chapter 1 and Chapter 2 sec 1ex: No lectures about section 3. The following announcements of this type have been made: Read as necessary, depending on your knowledge of topology. Harmonic functions, Poisson kernel. Exponential and Trigonometric functions. Homework 12 due Monday, Apr 11 — Products Sec 5. Poisson Integral, Schwarz reflection.

# Complex Variables

Poisson Integral, Schwarz reflection Chapter 4. There will be a total of eight problems on the exam, and you will be asked to complete any five of them. There are countless xourse tutorials, references, and resources, but these simple templates might help you get started: Naalysis final grade will be based on the midterm and final exam and the homework grades.

Quick review of elementary point set topology. Homework assignments will appear on this page approximately every week.

Normal Families Equicontinuity and Compactness.

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.

Problems are listed using notation like Sec 1.

Course Outline – Mat – Fall The sections under discussion will be announced in each lecture, and it is up to you to keep up with the corresponding reading. Cambridge University Press, Reading By the end of the first week, read chapter 1 and co,plex first two sections from chapter 2. Gamelin Bak and Newman.

Weekly homework Suggested exercises — Elliptic Functions Sec 7. Chapter 2, sec 1.

## CHEAT SHEET

That is, each challenge problem is worth as much as a weekly homework assignment! Unless otherwise noted, all problems refer to the main textbook, Complex Analysis3 rd Edition, by Lars Ahlfors. Final Exam in class.

Some of the material can also be found in Hyperbolic Geometry from a local viewpoint, L.