Handbook of Conformal Mappings and Applications

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.