ABSTRACT

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 I|1 pages

Theory and Conformal Maps

chapter 1|10 pages

Introduction

chapter 2|36 pages

Conformal Mapping

chapter 3|52 pages

Linear and Bilinear Transformations

chapter 4|38 pages

Algebraic Functions

chapter 5|54 pages

Exponential Family of Functions

chapter 6|14 pages

Joukowski Airfoils

chapter 7|54 pages

Schwarz-Christoffel Transformations

part 2|1 pages

Numerical Conformal Mapping

chapter 8|40 pages

Schwarz-Christoffel Integrals

chapter 9|22 pages

Nearly Circular Regions

chapter 10|30 pages

Integral Equation Methods

chapter 11|38 pages

Theodorsen’s Integral Equation

chapter 12|24 pages

Symm’s Integral Equation

chapter 13|34 pages

Airfoils and Singularities

chapter 14|36 pages

Doubly Connected Regions

chapter 15|14 pages

Multiply Connected Regions

part 3|1 pages

Applications

chapter 16|18 pages

Grid Generation

chapter 17|32 pages

Field Theories

chapter 18|44 pages

luid Flows

chapter 19|34 pages

Heat Transfer

chapter 20|26 pages

Vibrations and Acoustics

chapter 21|28 pages

Electromagnetic Field

chapter 22|40 pages

Transmission Lines and Waveguides

chapter 23|7 pages

Elastic Medium

chapter 24|52 pages

Finite Element Method

chapter 25|8 pages

Computer Programs and Resources