Complex Analysis with Applications / Edition 1

Complex Analysis with Applications / Edition 1

1.0 1
by Richard A. Silverman, Wendy Silverman, Mathematics
     
 

ISBN-10: 0486647625

ISBN-13: 9780486647623

Pub. Date: 10/18/2010

Publisher: Dover Publications

This basic book on functions of a complex variable represents the irreducible minimum of what every scientist and engineer should know about this important subject. From a preliminary discussion of complex numbers and functions to key topics such as the Cauchy theory, power series, and residues, distinguished mathematical writer Richard Silverman presents the

Overview

This basic book on functions of a complex variable represents the irreducible minimum of what every scientist and engineer should know about this important subject. From a preliminary discussion of complex numbers and functions to key topics such as the Cauchy theory, power series, and residues, distinguished mathematical writer Richard Silverman presents the fundamentals of complex analysis in a concise manner designed not to overwhelm the beginner. The author's lively style and simplicity of approach enable the reader to grasp essential topics without being distracted by secondary issues.
Contents include: Complex Numbers; Some Special Mapping; Limits in the Complex Plane; Multiple-Valued Functions' Complex Functions; Taylor Series; Differentiation in the Complex Plane; Laurent Series; Integration in the Complex Plane; Applications of Residues; Complex Series; Mapping of Polygonal Domains; Power Series; and Some Physical Applications.
Abundant exercise material and examples, as well as section-by-section comments at the end of each chapter make this book especially valuable to students and anyone encountering complex analysis for the first time.

Product Details

ISBN-13:
9780486647623
Publisher:
Dover Publications
Publication date:
10/18/2010
Series:
Dover Books on Mathematics Series
Edition description:
Dover ed
Pages:
304
Product dimensions:
5.39(w) x 8.44(h) x 0.60(d)

Table of Contents

Preface
1. Complex Numbers
  1.1. Basic Concepts
  1.2. The Complex Plane
  1.3. The Modulus and Argument
  1.4. Inversion
    Comments
    Problems
2. Limits in the Complex Plane
  2.1. The Principle of Nested Rectangles
  2.2. Limit Points
  2.3. Convergent Complex Sequences
  2.4. The Riemann Sphere and the Extended Complex Plane
    Comments
    Problems
3. Complex Functions
  3.1. Basic Concepts
  3.2. Curves and Domains
  3.3. Continuity of a Complex Function
  3.4. Uniform Continuity
    Comments
    Problems
4. Differentiation in the Complex Plane
  4.1. The Derivative of a Complex Function
  4.2. The Cauchy-Riemann Equations
  4.3. Conformal Mapping
    Comments
    Problems
5. Integration in the Complex Plane
  5.1. The Integral of a Complex Function
  5.2. Basic Properties of the Integral
  5.3. Integrals along Polygonal Curves
  5.4. Cauchy's Integral Theorem
  5.5. Indefinite Complex Integrals
  5.6. Cauchy's Integral Formula
  5.7. Infinite Differentiability of Analytic Functions
  5.8. Harmonic Functions
    Comments
    Problems
6. Complex Series
  6.1. Convergence vs. Divergence
  6.2. Absolute vs. Conditional Convergence
  6.3. Uniform Convergence
    Comments
    Problems
7. Power Series
  7.1. Basic Theory
  7.2. Determination of the Radius of Convergence
    Comments
    Problems
8. Some Special Mappings
  8.1. The Exponential and Related Functions
  8.2. Fractional Linear Transformations
    Comments
    Problems
9. Multiple-Valued Functions
  9.1. Domains of Univalence
  9.2. Branches and Branch Points
  9.3. Riemann Surfaces
    Comments
    Problems
10. Taylor Series
  10.1. The Taylor Expansion of an Analytic Function
  10.2. Uniqueness Theorems
  10.3. The Maximum Modulus Principle and Its Implications
    Comments
    Problems
11. Laurent Series
  11.1. The Laurent Expansion of an Analytic Function
  11.2. Isolated Singular Points
  11.3. Residues
    Comments
    Problems
12. Applications of Residues
  12.1. Logarithmic Residues and the Argument Principle
  12.2. Rouché's Theorem and Its Implications
  12.3. Evaluation of Improper Real Integrals
  12.4. Integrals Involving Multiple-Valued Functions
    Comments
    Problems
13. Further Theory
  13.1. More on Harmonic Functions
  13.2. The Dirichlet Problem
  13.3. More Conformal Mapping
  13.4. Analytic Continuation
  13.5. The Symmetry Principle
    Comments
    Problems
14. Mapping of Polygonal Domains
  14.1. The Schwarz-Christoffel Transformation
  14.2. Examples
    Comments
    Examples
15. Some Physical Applications
  15.1. Fluid Dynamics
  15.2. Examples
  15.3. Electrostatics
    Comments
    Problems
Selcted Hints and Answers
Bibliography
Index

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Complex Analysis with Applications 1 out of 5 based on 0 ratings. 1 reviews.
Guest More than 1 year ago
Written by somebody who knows his subject way to well to be able to communicate with someone just learning. Even after learning the material, his writing is frequently too thick to understand. Few useful example problems.