Complex Analysis III

(15-Math-6005)

Riemann sphere, Möbius transformations, Cauchy-Riemann equations, Cauchy's Theorems & Integral Formulas, Argument Principle, The Residue Theorem, Riemann Mapping Theorem, Schwarz Christoffel Formula

Department of

Mathematical

Sciences

This page is a work in progress! (Last revised 20 August 2013)

Instructor Prof David A Herron
4514 French Hall West 556-4075 		My Office Hours
TBA; and by appt 		E-mail me at David's e-address
My web page is at David's w-address

Basic Course Information

Textbooks There are zillions of books about Complex Analysis available in the Geo-Math-Physics Library. Below I list some texts which I think are pretty good. For our class, I will follow the book A First Course in Complex Analysis by Matthias Beck, Gerald Marchesi, Dennis Pixton, and Lucas Sabalka; a free pdf is available at here.

Here are links to pdf files for my class notes and a list of problems; these were for the Math 601 class (Complex Analysis I) that I taught in Fall Quarter 2009.

Sometimes it can be a good idea to look at more than one book/resource, because often some author will say things in just the 'right' way. Below I list some books that I know or have heard good things about.

The books by Ahlfors and Carathéodory are very geometric, which I quite like, but rather sophisticated. The book by Greene & Krantz is interesting and takes a novel approach. The books by McGehee and Palka are elementary with lotsa details presented. The books by Churchill & Brown, Greene & Krantz, McGehee, and Palka are all loaded with good problems. The book by Polya & Latta has some great parts too it.

P Palka An Introduction to Complex Function Theory
CB Churchill & Brown Complex Variables and Applications
GK Greene & Krantz Function Theory of One Complex Variable (second edition)
M McGehee An Introduction to Complex Analysis
PL Polya & Latta Complex Variable
A Ahlfors Complex Analysis (third edition)
C Carathéodory Theory of Functions (of a complex variable) Vols. I & II (second edition)

Also, do not overlook the web as a resource. For example, here are just two links to some more complex analysis pages: GA Tech, Fullerton.

General Syllabus Chapters 1-9 in the notes, plus possibly some additional material.

Exams and Important Dates

Grades

Your final course grade will be determined from your performance on the in class exams, a comprehensive final exam, your homework scores on written assignments, and your classroom and problem session participation. Here is a precise breakdown:

The Final Exam is scheduled for Monday December 9 at 1:30-3:30pm. The in-class hour exams are (tentatively) scheduled for Friday September 20, Friday October 18 and Wednesday November 13..

Homework

Unless I explicitly indicate otherwise, you should read everything in the text and try to work all of the exercises and problems that you find as you read. Any of these exercises, as well as all of the "fill in the details" that I mention during lectures, are fair game as "easy" exam questions.

Each week I will pass out a set of problems, many chosen from the text book. I will ask you write up and hand in solutions to certain of these exercises (aka, Homework); these will be graded and returned to you. Please be sure to check out my guidelines for writing up your HW solutions. Those problems not designated as Homework will be discussed at the weekly Problem Sessions. I will ask each of you to tell me which of the problems you have solved, and then I will select individuals to present their solutions at the board. I'll have more to say about this in class.

Here are some links to some interesting *things* such as videos, power point files, etc. I will add to this list as the year progresses.

Writing Mathematics

Class Stuff