# Handbook of Conformal Mapping with Computer-Aided Visualization

## Valentin I. Ivanov and Michael K. Trubetskov

1994

384 pages

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1994

384 pages

- 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 5.25" floppy disk for IBM-compatible computers that contains the
- CONFORM program.
- This book is addressed to students in applied mathematics studying complex
- analysis and its applications, and to specialists using CM for calculations
- of potential vector fields in science and engineering disciplines; also
- researchers, engineers, undergraduates, and postgraduates involved with
- aerodynamics, hydromechanics, hydraulics, elasticity, heat engineering,
- radioelectronics, and electron optics.

384 pages,1994

- 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