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cain g complex analysis 1999

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Textbook in PDF format 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. Title page and Table of Contents Chapter One - Complex Numbers (Introduction, Geometry, Polar coordinates) Chapter Two - Complex Functions (Functions of a real variable, Functions of a complex variable, Derivatives) Chapter Three - Elementary Functions (Introduction, The exponential function, Trigonometric functions, Logarithms and complex exponents) Chapter Four - Integration (Introduction, Evaluating integrals, Antiderivatives) Chapter Five - Cauchy's Theorem (Homotopy, Cauchy's Theorem) Chapter Six - More Integration (Cauchy's Integral Formula, Functions defined by integrals, Liouville's Theorem, Maximum moduli) Chapter Seven - Harmonic Functions (The Laplace equation, Harmonic functions, Poisson's integral formula) Chapter Eight - Series (Sequences, Series, Power series, Integration of power series, Differentiation of power series) Chapter Nine - Taylor and Laurent Series (Taylor series, Laurent series) Chapter Ten - Poles, Residues, and All That (Residues, Poles and other singularities, Applications of the Residue Theorem to Real Integrals-Supplementary) Chapter Eleven - Argument Principle (Argument principle, Rouche's Theorem)

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cain g complex analysis 1999