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9780486406794

Complex Variables Second Edition

by
  • ISBN13:

    9780486406794

  • ISBN10:

    0486406792

  • Edition: 2nd
  • Format: Paperback
  • Copyright: 1999-02-16
  • Publisher: Dover Publications

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Summary

Hundreds of solved examples, exercises, and applications help students gain a firm understanding of the most important topics in the theory and applications of complex variables. Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. Perfect for undergrads/grad students in science, mathematics, engineering. A three-semester course in calculus is sole prerequisite. 1990 edition. Appendices.

Table of Contents

The complex plane
The complex numbers and the complex plane
A formal view of the complex numbers
Some geometry
Subsets of the plane
Functions and limits
The exponential, logarithm, and trigonometric functions
Line integrals and Green's theorem
Basic properties of analytic functions
Analytic and harmonic functions; the Cauchy-Riemann equations
Flows, fields, and analytic functions
Power series
Cauchy's theorem and Cauchy's formula
The Cauchy-Goursat theorem
Consequences of Cauchy's formula
Isolated singularities
The residue theorem and its application to the evaluation of definite integrals
Analytic functions as mappings
The zeros of an analytic function
The stability of solutions of a system of linear differential equations
Maximum modulus and mean value
Linear fractional transformations
Conformal mapping
Conformal mapping and flows
The Riemann mapping theorem and Schwarz-Christoffel transformations
Analytic and harmonic functions in applications
Harmonic functions
Harmonic functions as solutions to physical problems
Integral representations of harmonic functions
Boundary-value problems
Impulse functions and the Green's function of a domain
Transform methods
The Fourier transform: basic properties
Formulas Relating u and u
The Laplace transform
Applications of the Laplace transform to differential equations
The Z-Transform
The stability of a discrete linear system
The stability of a discrete linear system
A Table of Conformal Mappings
A Table of Laplace Transforms
Solutions to Odd-Numbered Exercises
Index
Table of Contents provided by Publisher. All Rights Reserved.

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