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Analysis Complex Variables and Applications by Brown and Churchill

  1. Strongly Recommend

    50.0%
  2. Lightly Recommend

    25.0%
  3. Lightly don't Recommend

    0 vote(s)
    0.0%
  4. Strongly don't Recommend

    25.0%
  1. Feb 3, 2013 #1

    micromass

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    2016 Award


    Table of Contents:
    Code (Text):

    [LIST]
    [*] Preface
    [*] Complex Numbers
    [LIST]
    [*] Sums and Products
    [*] Basic Algebraic Properties
    [*] Further Properties
    [*] Vectors and Moduli
    [*] Complex Conjugates
    [*] Exponential Form
    [*] Products and Powers in Exponential Form
    [*] Arguments of Products and Quotients
    [*] Roots of Complex Numbers
    [*] Examples
    [*] Regions in the Complex Plane
    [/LIST]
    [*] Analytic Functions
    [LIST]
    [*] Functions of a Complex Variable
    [*] Mappings
    [*] Mappings by the Exponential Function
    [*] Limits
    [*] Theorems on Limits
    [*] Limits Involving the Point at Infinity
    [*] Continuity
    [*] Derivatives
    [*] Differentiation Formulas
    [*] Cauchy-Riemann Equations
    [*] Sufficient Conditions for Differentiability
    [*] Polar Coordinates
    [*] Analytic Functions
    [*] Examples
    [*] Harmonic Functions
    [*] Uniquely Determined Analytic Functions
    [*] Reflection Principle
    [/LIST]
    [*] Elementary Functions
    [LIST]
    [*] The Exponential Function
    [*] The Logarithmic Function
    [*] Branches and Derivatives of Logarithms
    [*] Some Identities Involving Logarithms
    [*] Complex Exponents
    [*] Trigonometric Functions
    [*] Hyperbolic Functions
    [*] Inverse Trigonometric and Hyperbolic Functions
    [/LIST]
    [*] Integrals
    [LIST]
    [*] Derivatives of Functions w(t)
    [*] Definite Integrals of Functions w(t)
    [*] Contours
    [*] Contour Integrals
    [*] Some Examples
    [*] Examples with Branch Cuts
    [*] Upper Bounds for Moduli of Contour Integrals
    [*] Antiderivatives
    [*] Proof of the Theorem
    [*] Cauchy-Goursat Theorem
    [*] Proof of the Theorem
    [*] Simply Connected Domains
    [*] Multiply Connected Domains
    [*] Cauchy Integral Formula
    [*] An Extension of the Cauchy Integral Formula
    [*] Some Consequences of the Extension
    [*] Liouville's Theorem and the Fundamental Theorem of Algebra
    [*] Maximum Modulus Principle
    [/LIST]
    [*] Series
    [LIST]
    [*] Convergence of Sequences
    [*] Convergence of Series
    [*] Taylor Series
    [*] Proof of Taylor's Theorem
    [*] Examples
    [*] Laurent Series
    [*] Proof of Laurent's Theorem
    [*] Examples
    [*] Absolute and Uniform Convergence of Power Series
    [*] Continuity of Sums of Power Series
    [*] Integration and Differentiation of Power Series
    [*] Uniqueness of Series Representations
    [*] Multiplication and Division of Power Series
    [/LIST]
    [*] Residues and Poles
    [LIST]
    [*] Isolated Singular Points
    [*] Residues
    [*] Cauchy's Residue Theorem
    [*] Residue at Infinity
    [*] The Three Types of Isolated Singular Points
    [*] Residues at Poles
    [*] Examples
    [*] Zeros of Analytic Functions
    [*] Zeros and Poles
    [*] Behavior of Functions Near Isolated Singular Points
    [/LIST]
    [*] Applications of Residues
    [LIST]
    [*] Evaluation of Improper Integrals
    [*] Example
    [*] Improper Integrals from Fourier Analysis
    [*] Jordan's Lemma
    [*] Indented Paths
    [*] An Indentation Around a Branch Point
    [*] Integration Along a Branch Cut
    [*] Definite Integrals Involving Sines and Cosines
    [*] Argument Principle
    [*] Rouché's Theorem
    [*] Inverse Laplace Transforms
    [*] Examples
    [/LIST]
    [*] Mapping by Elementary Functions
    [LIST]
    [*] Linear Transformations
    [*] The Transformation w = 1/z
    [*] Mappings by 1/z
    [*] Linear Fractional Transformations
    [*] An Implicit Form
    [*] Mappings of the Upper Half Plane
    [*] The Transformation w = sin z
    [*] Mappings by z^2 and Branches of z^{1/2}
    [*] Square Roots of Polynomials
    [*] Riemann Surfaces
    [*] Surfaces for Related Functions
    [/LIST]
    [*] Conformal Mapping
    [LIST]
    [*] Preservation of Angles
    [*] Scale Factors
    [*] Local Inverses
    [*] Harmonic Conjugates
    [*] Transformations of Harmonic Functions
    [*] Transformations of Boundary Conditions
    [/LIST]
    [*] Applications of Conformal Mapping
    [LIST]
    [*] Steady Temperatures
    [*] Steady Temperatures in a Half Plane
    [*] A Related Problem
    [*] Temperatures in a Quadrant
    [*] Electrostatic Potential
    [*] Potential in a Cylindrical Space
    [*] Two-Dimensional Fluid Flow
    [*] The Stream Function
    [*] Flows Around a Corner and Around a Cylinder
    [/LIST]
    [*] The Schwarz--Christoffel Transformation
    [LIST]
    [*] Mapping the Real Axis Onto a Polygon
    [*] Schwarz--Christoffel Transformation
    [*] Triangles and Rectangles
    [*] Degenerate Polygons
    [*] Fluid Flow in a Channel Through a Slit
    [*] Flow in a Channel With an Offset
    [*] Electrostatic Potential About an Edge of a Conducting Plate
    [/LIST]
    [*] Integral Formulas of the Poisson Type
    [LIST]
    [*] Poisson Integral Formula
    [*] Dirichlet Problem for a Disk
    [*] Related Boundary Value Problems
    [*] Schwarz Integral Formula
    [*] Dirichlet Problem for a Half Plane
    [*] Neumann Problems
    [/LIST]
    [*] Appendixes
    [LIST]
    [*] Bibliography
    [*] Table of Transformations of Regions
    [/LIST]
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 3, 2013 #2
    Solid user-friendly intro book on complex variables, sort of a rough equivalent to linear algebra done right.
     
  4. Feb 3, 2013 #3
    I'd highly recommend for a physics or chemistry student who wants a better grasp of residues and conformal mappings, but which is not too mathematically intense.
     
  5. Feb 4, 2013 #4
    This is a decent introductory book, geared well toward physicists and engineers but rigorous enough to not offend a math-major. It is clearly written and organized, making it decent as a reference book.

    However, it doesn't give much insight into the beauty of the subject. This is a common required textbook for intro courses, so I recommend also getting Visual Complex Analysis as an interesting supplementary text.

    There is also a solid free textbook here:
    http://www.math.uiuc.edu/~r-ash/CV.html

    I am familliar with the author's abstract algebra book (which I like), but I have only skimmed parts of this one.
     
  6. Feb 4, 2013 #5

    jasonRF

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    I am familiar with the 5th edition, which I have had for about 20 years. I think it is a reasonable book that covers most of the material many engineers/physicists need for routine applications. By far my favorite sections are those on conformal mapping - the presentation is quite good for applications. In most ways Churchill and Brown is better than the book I had to buy for my complex analysis class (introduction to complex analysis, by Priestley), but I am not wild about the organization of most of the book. Overall I prefer the book by Saff and Snider for an introduction.
     
  7. Mar 1, 2013 #6
    I studied the first ten chapters of this book (omitting the final chapters on applications). I used the seventh edition (the eighth edition is now the most current one). I found this text to be ideal for someone (such as myself) who had studied complex analysis a long time ago and wanted to relearn it. The text is almost entirely free of typos and errors, which I find to be important for self-study. The proofs are clear and the examples well-chosen. The exercises are primarily calculations, with a few simple proofs thrown in. This is not a criticism; I found some of the calculations to be challenging. Someone who wants to study more advanced topics in Complex Analysis should consult a second book, such as Lang, Ahlfors or Conway (after studying this text).
     
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