Handbook of Conformal Mappings and Applications  book cover
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Handbook of Conformal Mappings and Applications





ISBN 9781138748477
Published March 4, 2019 by Chapman and Hall/CRC
942 Pages 530 B/W Illustrations

 
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Book Description

The subject of conformal mappings is a major part of geometric function theory that gained prominence after the publication of the Riemann mapping theorem — for every simply connected domain of the extended complex plane there is a univalent and meromorphic function that maps such a domain conformally onto the unit disk. The Handbook of Conformal Mappings and Applications is a compendium of at least all known conformal maps to date, with diagrams and description, and all possible applications in different scientific disciplines, such as: fluid flows, heat transfer, acoustics, electromagnetic fields as static fields in electricity and magnetism, various mathematical models and methods, including solutions of certain integral equations.

Table of Contents

Part 1: Theory and Conformal Maps



1 Introduction



2 Conformal Mapping



3 Linear and Bilinear Transformations



4 Algebraic Functions



5 Exponential Family of Functions



6 Joukowski Airfoils



7 Schwarz-Christoffel Transformation



Part 2: Numerical Methods



8 Schwarz-Christoffel Integrals



9 Nearly Circular Regions



10 Integral Equation Methods



11 Theodorsen’s Integral Equation



12 Symm’s Integral Equation



13 Airfoils and Singularities



14 Doubly Connected Regions



15 Multiply Connected Regions



Part 3: Applications



16 Grid Generation



17 Field Theories



18 Fluid Flows



19 Heat Transfer



20 Vibrations and Acoustics



21 Electromagnetic Field



22 Transmission Lines and Waveguides



23 Elastic Medium



24 Finite Element Method



25 Computer Programs and Resources

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Author(s)

Biography

Prem K. Kythe is a Professor Emeritus of Mathematics at the University of New Orleans. He is the author/co-author of 12 books and author of 46 research papers. His research interests encompass the fields of complex analysis, continuum mechanics, and wave theory, including boundary element methods, finite element methods, conformal mappings, PDEs and boundary value problems, linear integral equations, computation integration, fundamental solutions of differential operators, Green’s functions, and coding theory.