1st Edition

Handbook of Conformal Mappings and Applications

By Prem K. Kythe Copyright 2019
    944 Pages
    by Chapman & Hall

    942 Pages 530 B/W Illustrations
    by Chapman & Hall

    942 Pages 530 B/W Illustrations
    by Chapman & Hall

    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.

    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

    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.