# Basic Complex Analysis by by J. E. Marsden and M.J. Hoffman

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## Main Question or Discussion Point

Code:
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[*] Analytic Functions
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[*] Introduction to Complex Numbers
[*] Properties of Complex Numbers
[*] Some Elementary Functions
[*] Continuous Functions
[*] Basic Properties of Analytic Functions
[*] Differentiation of the Elementary Functions
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[*] Cauchy's Theorem
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[*] Contour Integrals
[*] Cauchy's Theorem—A First Look
[*] A Closer Look at Cauchy's Theorem
[*] Cauchy's Integral Formula
[*] Maximum Modulus Theorem and Harmonic Functions
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[*] Series Representation of Analytic Functions
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[*] Convergent Series of Analytic Functions
[*] Power Series and Taylor's Theorem
[*] Laurent Series and Classification of Singularities
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[*] Calculus of Residues
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[*] Calculation of Residues
[*] Residue Theorem
[*] Evaluation of Definite Integrals
[*] Evaluation of Infinite Series and Partial-Fraction Expansions
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[*] Conformal Mappings
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[*] Basic Theory of Conformal Mappings
[*] Fractional Linear and Schwarz-Christoffel Transformations
[*] Applications of Conformal Mappings to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics
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[*] Further Development of the Theory
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[*] Analytic Continuation and Elementary Riemann Surfaces
[*] Rouche's Theorem and Principle of the Argument
[*] Mapping Properties of Analytic Functions
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[*] Asymptotic Methods
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[*] Infinite Products and the Gamma Function
[*] Asymptotic Expansions and the Method of Steepest Descent
[*] Stirling's Formula and Bessel Functions
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[*] Laplace Transform and Applications
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[*] Basic Properties of Laplace Transforms
[*] Complex Inversion Formula
[*] Application of Laplace Transforms to Ordinary Differential Equations
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[*] Index
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