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


    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.