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 Complex Analysis  posted by  member7_php   on 4/2/2009  Add Courseware to favorites Add To Favorites  
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Complex Analysis


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.

The notes are available as Adobe Acrobat documents. If you do not have an Adobe Acrobat Reader, you may down-load a copy, free of charge, from Adobe.

Title page and Table of Contents

Table of Contents

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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