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Complex Analysis with Applications

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Complex Analysis with Applications Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.

About 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.

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

Product Details

ISBN:
9780486647623
Author:
Silverman, Richard A.
Publisher:
Dover Publications
Author:
Mathematics
Author:
Silverman, Jerry
Location:
New York :
Subject:
General
Subject:
Mathematics
Subject:
Calculus
Subject:
Advanced
Subject:
Functions of complex variables
Subject:
General Mathematics
Subject:
Functional Analysis
Subject:
Mathematics-Calculus
Copyright:
Edition Number:
Dover ed.
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
no. 4
Publication Date:
20101031
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
304
Dimensions:
8.5 x 5.38 in 0.71 lb

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Related Subjects

Reference » Science Reference » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Complex Analysis
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Real Analysis
Science and Mathematics » Mathematics » Topology

Complex Analysis with Applications New Trade Paper
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Product details 304 pages Dover Publications - English 9780486647623 Reviews:
"Synopsis" by ,
The basics of what every scientist and engineer should know, 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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