Complex Analysis and Applications

Complex Analysis and Applications

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Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the theory of complex analysis, and then examines its geometrical interpretation and application to Dirichlet and Neumann boundary value problems. A discussion of complex analysis now forms the first three chapters of the book, with a description of conformal mapping and its application to boundary value problems for the two-dimensional Laplace equation forming the final two chapters. This new structure enables students to study theory and applications separately, as needed. In order to maintain brevity and clarity, the text limits the application of complex analysis to two-dimensional boundary value problems related to temperature distribution, fluid flow, and electrostatics. In each case, in order to show the relevance of complex analysis, each application is preceded by mathematical background that demonstrates how a real valued potential function and its related complex potential can be derived from the mathematics that describes the physical situation.
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Product details

  • Paperback | 592 pages
  • 165.1 x 241.3 x 35.6mm | 975.23g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • 204 black & white illustrations, 1 black & white tables
  • 158488553X
  • 9781584885535
  • 2,518,543

Table of contents

Analytic Functions Review of Complex Numbers Curves, Domains, and Regions Analytic Functions The Cauchy-Riemann Equations: Proof and Consequences Elementary Functions Complex Integration Contours and Complex Integrals The Cauchy Integral Theorem Antiderivatives and Definite Integrals The Cauchy Integral Formula The Cauchy Integral Formula for Derivatives Useful Results Deducible from the Cauchy Integral Formulas Evaluation of Improper Integrals by Contour Integration Taylor and Laurent Series: Residue Theorem and Applications Sequences, Series, and Convergence Uniform Convergence Power Series Taylor Series Laurent Series Classification of Singularities and Zeros Residues and the Residue Theorem Applications of the Residue Theorem The Laplace Inversion Integral Conformal Mapping Geometrical Aspects of Analytic Functions: Mapping Conformal Mapping The Linear Fractional Transformation Mappings by Elementary Functions The Schwarz-Christoffel Transformation Boundary Value Problems, Potential Theory, and Conformal Mapping Laplace's Equation and Conformal Mapping - Boundary Value Problems Standard Solutions of the Laplace Equation Steady-State Two-Dimensional Temperature Distribution Steady Two-Dimensional Fluid Flow Two-Dimensional Electrostatics
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