Complex Analysis with Applications / Edition 1

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This volume contains the basics of what every scientist and engineer should know about complex analysis. A lively style combined with a simple, direct approach helps readers grasp the fundamentals, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.

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Product Details

  • ISBN-13: 9780486647623
  • Publisher: Dover Publications
  • Publication date: 10/18/2010
  • Series: Dover Books on Mathematics Series
  • Edition description: Dover ed
  • Edition number: 1
  • Pages: 304
  • Product dimensions: 5.39 (w) x 8.44 (h) x 0.60 (d)

Meet the Author

Richard A. Silverman: Dover's Trusted Advisor
Richard Silverman was the primary reviewer of our mathematics books for well over 25 years starting in the 1970s. And, as one of the preeminent translators of scientific Russian, his work also appears in our catalog in the form of his translations of essential works by many of the greatest names in Russian mathematics and physics of the twentieth century. These titles include (but are by no means limited to): Special Functions and Their Applications (Lebedev); Methods of Quantum Field Theory in Statistical Physics (Abrikosov, et al); An Introduction to the Theory of Linear Spaces, Linear Algebra, and Elementary Real and Complex Analysis (all three by Shilov); and many more.

During the Silverman years, the Dover math program attained and deepened its reach and depth to a level that would not have been possible without his valuable contributions.

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Table of Contents

1. Complex Numbers
  1.1. Basic Concepts
  1.2. The Complex Plane
  1.3. The Modulus and Argument
  1.4. Inversion
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
3. Complex Functions
  3.1. Basic Concepts
  3.2. Curves and Domains
  3.3. Continuity of a Complex Function
  3.4. Uniform Continuity
4. Differentiation in the Complex Plane
  4.1. The Derivative of a Complex Function
  4.2. The Cauchy-Riemann Equations
  4.3. Conformal Mapping
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
6. Complex Series
  6.1. Convergence vs. Divergence
  6.2. Absolute vs. Conditional Convergence
  6.3. Uniform Convergence
7. Power Series
  7.1. Basic Theory
  7.2. Determination of the Radius of Convergence
8. Some Special Mappings
  8.1. The Exponential and Related Functions
  8.2. Fractional Linear Transformations
9. Multiple-Valued Functions
  9.1. Domains of Univalence
  9.2. Branches and Branch Points
  9.3. Riemann Surfaces
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
11. Laurent Series
  11.1. The Laurent Expansion of an Analytic Function
  11.2. Isolated Singular Points
  11.3. Residues
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
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
14. Mapping of Polygonal Domains
  14.1. The Schwarz-Christoffel Transformation
  14.2. Examples
15. Some Physical Applications
  15.1. Fluid Dynamics
  15.2. Examples
  15.3. Electrostatics
Selcted Hints and Answers
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  • Anonymous

    Posted August 30, 2000

    Terrible, terrible book

    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.

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