## Handbook of Conformal Mapping with Computer-Aided VisualizationThis 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. |

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### Contents

the Theory of Conformal Mappings | 9 |

Applications of Conformal Mappings | 241 |

Catalog of Conformal Mappings | 291 |

Program CONFORM | 337 |

345 | |

357 | |

### Common terms and phrases

analytic continuation analytic function arctan arth boundary point branch points called canonical domain Cartesian Cassini's oval Cauchy-Riemann conditions complex number complex potential composition of functions conformal mapping considered domain coordinates cosh Create the mapping curvilinear angular domain curvilinear strip cylinder depicted in Fig domain bounded domain G doubly connected doubly connected domain elementary functions elliptic integral equation Example extended complex plane exterior finite domain formula func Function Comment Figure function f(z hyperbola integer angles inverse mapping isothermic Jordan curve Let the function linear-fractional function linear-fractional transformation map the domain maps the half-plane obtained parabola parameter point at infinity point Z0 pole polygonal domain presented in Fig program CONFORM quadrangle real axis reciprocal one-to-one relief map represents satisfying the condition Schwarz-Christoffel integral segment shown in Fig singly connected domain straight line Subsection symmetrical theorem tion traversal unit circle univalent upper half-plane values vector field velocity field z-plane Zhukovskii function

### Popular passages

Page 351 - Lavrentiev, MA, Shabat, BV Problems of Hydrodynamics and Their Mathematical Models, Nauka, Moscow, 1977, (in Russian).