Complex variables /

Complex variables /

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Bibliographic Details
Author / Creator:Fisher, Stephen D., 1941-
Edition:2nd ed.
Imprint:Mineola, N.Y. : Dover, 1999.
Description:xiv, 427 p. : ill. ; 24 cm.
Language:English
Series:Dover books on mathematics
Subject:
Functions of complex variables.
Functions of complex variables.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/6215645
Hidden Bibliographic Details
ISBN:0486406792 (pbk.)
Notes:"This Dover edition, first published in 1999, is a slightly corrected, unabridged republication of the work originally published in 1990 by Wadsworth & Brooks, Pacific Grove, California"--T.p. verso.
Includes bibliographical references and index.
Table of Contents:
  • 1. The complex plane
  • 1.1. The complex numbers and the complex plane
  • 1.1.1. A formal view of the complex numbers
  • 1.2. Some geometry
  • 1.3. Subsets of the plane
  • 1.4. Functions and limits
  • 1.5. The exponential, logarithm, and trigonometric functions
  • 1.6. Line integrals and Green's theorem
  • 2. Basic properties of analytic functions
  • 2.1. Analytic and harmonic functions; the Cauchy-Riemann equations
  • 2.1.1. Flows, fields, and analytic functions
  • 2.2. Power series
  • 2.3. Cauchy's theorem and Cauchy's formula
  • 2.3.1. The Cauchy-Goursat theorem
  • 2.4. Consequences of Cauchy's formula
  • 2.5. Isolated singularities
  • 2.6. The residue theorem and its application to the evaluation of definite integrals
  • 3. Analytic functions as mappings
  • 3.1. The zeros of an analytic function
  • 3.1.1. The stability of solutions of a system of linear differential equations
  • 3.2. Maximum modulus and mean value
  • 3.3. Linear fractional transformations
  • 3.4. Conformal mapping
  • 3.4.1. Conformal mapping and flows
  • 3.5. The Riemann mapping theorem and Schwarz-Christoffel transformations
  • 4. Analytic and harmonic functions in applications
  • 4.1. Harmonic functions
  • 4.2. Harmonic functions as solutions to physical problems
  • 4.3. Integral representations of harmonic functions
  • 4.4. Boundary-value problems
  • 4.5. Impulse functions and the Green's function of a domain
  • 5. Transform methods
  • 5.1. The Fourier transform: basic properties
  • 5.2. Formulas Relating u and u
  • 5.3. The Laplace transform
  • 5.4. Applications of the Laplace transform to differential equations
  • 5.5. The Z-Transform
  • 5.5.1. The stability of a discrete linear system
  • Appendix 1. The stability of a discrete linear system
  • Appendix 2. A Table of Conformal Mappings
  • Appendix 3. A Table of Laplace Transforms
  • Solutions to Odd-Numbered Exercises
  • Index

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