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This book is a guide on conformal mappings, their applications in physics and technology, and their computer-aided visualization. Conformal mapping (CM) is a classical part of complex analysis having numerous applications to mathematical physics. This modern handbook on CM includes recent results such as the classification of all triangles and quadrangles that can be mapped by elementary functions, mappings realized by elliptic integrals and Jacobian elliptic functions, and mappings of doubly connected domains. This handbook considers a wide array of applications, among which are the construction of a Green function for various boundary-value problems, streaming around airfoils, the impact of a cylinder on the surface of a liquid, and filtration under a dam. With more than 160 domains included in the catalog of mapping, Handbook of Conformal Mapping with Computer-Aided Visualization is more complete and useful than any previous volume covering this important topic. The authors have developed an interactive ready-to-use software program for constructing conformal mappings and visualizing plane harmonic vector fields. The book includes a floppy disk for IBM-compatible computers that contains the CONFORM program.
Table of Contents
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