Handbook of Conformal Mapping with Computer-Aided Visualization

Valentin I. Ivanov and Michael K. Trubetskov

(1994) 384 pages

This book is a guide on conformal mappings, their applications in physicsand technology, and their computer-aided visualization. Conformal mapping(CM) is a classical part of complex analysis having numerous applications tomathematical physics. This modern handbook on CM includes recent resultssuch as the classification of all triangles and quadrangles that can bemapped by elementary functions, mappings realized by elliptic integrals andJacobian elliptic functions, and mappings of doubly connected domains. Thishandbook considers a wide array of applications, among which are theconstruction of a Green function for various boundary-value problems,streaming around airfoils, the impact of a cylinder on the surface of aliquid, and filtration under a dam.

With more than 160 domains included in the catalog of mapping, Handbook ofConformal Mapping with Computer-Aided Visualization is more complete anduseful than any previous volume covering this important topic. The authorshave developed an interactive ready-to-use software program for constructingconformal mappings and visualizing plane harmonic vector fields. The bookincludes a 5.25" floppy disk for IBM-compatible computers that contains theCONFORM program.

This book is addressed to students in applied mathematics studying complexanalysis and its applications, and to specialists using CM for calculationsof potential vector fields in science and engineering disciplines; alsoresearchers, engineers, undergraduates, and postgraduates involved withaerodynamics, hydromechanics, hydraulics, elasticity, heat engineering,radioelectronics, and electron optics.

384 pages,1994

Features Unique representations of the results assisted by computer examples.; Method for the computer visualization of potential vector fields, developed and applied by the authors.; Includes 5.25" computer disk of CONFORM, an original program in Windows[registration mark] that contains all mappings in the book and helps the reader visualize new ones.

* Mathematics: The Theory of Conformal Mappings; * Complex Plane, Domains and Curves on It; * The Analytic Functions of a Complex Variable; * Conjugate Harmonic Functions; * The Geometric Meaning of the Derivative; Isogonal and Local Conformal; Mappings; * Univalent Analytic Functions. Conformal Mappings of Domains; * General Principles of the Theory of Conformal Mappings; * Conformal Mappings Realized by the Basic Elementary Functions; * Isothermic Coordinates. Differential Operators in the Isothermic; Coordinates; * Mappings of Lunes; * The Construction of Conformal Mappings with the Help of the Boundary; Correspondence Principle; * The Construction of Conformal Mappings of Curvilinear Strips with the; Help of an Analytic Continuation of a Function from the Real Axis; * The Mapping of Polygonal Domains. Schwarz-Christoffel Integral; * Mappings of Rectangular Domains. Elliptic Integrals and Elliptic; Functions; * Conformal Mapping of Doubly Connected Domains; * Physics: Applications of Conformal Mappings; * Insight into Plane Harmonic Vector Field; * Plane Harmonic Vector Fields in Physics; * Complex Potential; * Boundary-Value Problems for Harmonic Functions; * The Construction of a Green Function of the Dirichlet Problem; * The Green Function of the Neumann Problem; * The Green Function of a Mixed Boundary-Value Problem; * Point Source and Sink in the Dirichlet Problem; * Point Source and Sink in the Neumann Problem; * Plane Robin Problem; * The Flow in a Curvilinear Angular Domain. Streaming Around an Infinite; Curve; * The Flow in a Curvilinear Strip; * The Flow in a Curvilinear Strip with N Branches; * The Flow Running onto an Infinite Curve and Branching on It; * Irrotational Streaming Around a Finite Contour; * Mixed Boundary-Value Problem in a Curvilinear Angular Domain. The; Simplest Problem of the Filtration Theory; * Distribution of the Electric Current in a Plate in the Presence of Two; Non-Point Electrodes at Its Boundary; * The General Problem on the Streaming Around a Finite Contour; * The Problem on the Impact of a Solid Cylinder upon the Surface of a; Non-Compressible Liquid; * The Flow with Branching in a Curvilinear Strip with N Branches; * Practice: Catalog of Conformal Mappings; * Finite Domains; * Exteriors of Finite Contours; * Curvilinear Angular Domains; * Curvilinear Strips; * Curvilinear Strips with N Branches; * Appendix: Program CONFORM