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 Complex Analysis  posted by  member7_php   on 4/2/2009 Add To Favorites
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Abstract/Syllabus:

## by

### George Cain

This is a textbook for an introductory course in complex analysis. It has been used for our undergraduate complex analysis course here at Georgia Tech and at a few other places that I know of.

I owe a special debt of gratitude to Professor Matthias Beck of SUNY Binghamton who used the book in his class at Binghamton and found many errors and made many good suggestions for changes and additions to the book. I thank him very much. I have corrected the errors and made some changes.

I am also grateful to Professor Pawel Hitczenko of Drexel University, who prepared the nice supplement to Chapter 10 on applications of the Residue Theorem to real integration.

#### Chapter One - Complex Numbers

1.1 Introduction
1.2 Geometry
1.3 Polar coordinates

#### Chapter Two - Complex Functions

2.1 Functions of a real variable
2.2 Functions of a complex variable
2.3 Derivatives

#### Chapter Three - Elementary Functions

3.1 Introduction
3.2 The exponential function
3.3 Trigonometric functions
3.4 Logarithms and complex exponents

#### Chapter Four - Integration

4.1 Introduction
4.2 Evaluating integrals
4.3 Antiderivatives

#### Chapter Five - Cauchy's Theorem

5.1 Homotopy
5.2 Cauchy's Theorem

#### Chapter Six - More Integration

6.1 Cauchy's Integral Formula
6.2 Functions defined by integrals
6.3 Liouville's Theorem
6.4 Maximum moduli

#### Chapter Seven - Harmonic Functions

7.1 The Laplace equation
7.2 Harmonic functions
7.3 Poisson's integral formula

#### Chapter Eight - Series

8.1 Sequences
8.2 Series
8.3 Power series
8.4 Integration of power series
8.5 Differentiation of power series

#### Chapter Nine - Taylor and Laurent Series

9.1 Taylor series
9.2 Laurent series

#### Chapter Ten - Poles, Residues, and All That

10.1 Residues
10.2 Poles and other singularities

Applications of the Residue Theorem to Real Integrals-Supplementary Material by Pawel Hitczenko

#### Chapter Eleven - Argument Principle

11.1 Argument principle
11.2 Rouche's Theorem

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