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# ca - 7.1 The Laplace equation 7.2 Harmonic functions 7.3...

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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
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Unformatted text preview: 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 Chapter Eleven - Argument Principle 11.1 Argument principle 11.2 Rouche's Theorem----------------------------------------------------------------------------George Cain School of Mathematics Georgia Institute of Technology Atlanta, Georgia 0332-0160 [email protected]
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ca - 7.1 The Laplace equation 7.2 Harmonic functions 7.3...

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