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

  1. Strongly Recommend

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  2. Lightly Recommend

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  4. Strongly don't Recommend

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  1. Jan 20, 2013 #1

    Table of Contents:
    Code (Text):

    [LIST]
    [*] Analytic Functions
    [LIST]
    [*] Introduction to Complex Numbers
    [*] Properties of Complex Numbers
    [*] Some Elementary Functions
    [*] Continuous Functions
    [*] Basic Properties of Analytic Functions
    [*] Differentiation of the Elementary Functions
    [/LIST]
    [*] Cauchy's Theorem
    [LIST]
    [*] 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
    [/LIST]
    [*] Series Representation of Analytic Functions
    [LIST]
    [*] Convergent Series of Analytic Functions
    [*] Power Series and Taylor's Theorem
    [*] Laurent Series and Classification of Singularities
    [/LIST]
    [*] Calculus of Residues
    [LIST]
    [*] Calculation of Residues
    [*] Residue Theorem
    [*] Evaluation of Definite Integrals
    [*] Evaluation of Infinite Series and Partial-Fraction Expansions
    [/LIST]
    [*] Conformal Mappings
    [LIST]
    [*] Basic Theory of Conformal Mappings
    [*] Fractional Linear and Schwarz-Christoffel Transformations
    [*] Applications of Conformal Mappings to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics
    [/LIST]
    [*] Further Development of the Theory
    [LIST]
    [*] Analytic Continuation and Elementary Riemann Surfaces
    [*] Rouche's Theorem and Principle of the Argument
    [*] Mapping Properties of Analytic Functions
    [/LIST]
    [*] Asymptotic Methods
    [LIST]
    [*] Infinite Products and the Gamma Function
    [*] Asymptotic Expansions and the Method of Steepest Descent
    [*] Stirling's Formula and Bessel Functions
    [/LIST]
    [*] Laplace Transform and Applications
    [LIST]
    [*] Basic Properties of Laplace Transforms
    [*] Complex Inversion Formula
    [*] Application of Laplace Transforms to Ordinary Differential Equations
    [/LIST]
    [*] Answers to Odd-Numbered Exercises
    [*] Index
    [/LIST]
     
     
    Last edited: May 6, 2017
  2. jcsd
  3. Jan 21, 2013 #2
    I've tried over the last 5 years, many intro Complex Analysis text books and this one is by far the best one I've used. It's not overly-complicated, not too many proofs, and is a pleasant read compared to other text books which are difficult to follow. It presents the topics in a very accessible way that I believe the student can follow without difficulty.

    I would highly recommend this text as a second book for anyone taking the subject for the first time. I use my often.
     
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