Boundary Behaviour of Conformal Maps

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Publisher : Springer Science & Business Media
ISBN 13 : 3662027704
Total Pages : 307 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Boundary Behaviour of Conformal Maps by : Christian Pommerenke

Download or read book Boundary Behaviour of Conformal Maps written by Christian Pommerenke and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is to obtain a one-to-one correspondence between analytic properties of the function and geometrie properties of the domain. In the classical applications of conformal mapping, the domain is bounded by a piecewise smooth curve. In many recent applications however, the domain has a very bad boundary. It may have nowhere a tangent as is the case for Julia sets. Then the conformal map has many unexpected properties, for instance almost all the boundary is mapped onto almost nothing and vice versa. The book is meant for two groups of users. (1) Graduate students and others who, at various levels, want to learn about conformal mapping. Most sections contain exercises to test the understand ing. They tend to be fairly simple and only a few contain new material. Pre requisites are general real and complex analyis including the basic facts about conformal mapping (e.g. AhI66a). (2) Non-experts who want to get an idea of a particular aspect of confor mal mapping in order to find something useful for their work. Most chapters therefore begin with an overview that states some key results avoiding tech nicalities. The book is not meant as an exhaustive survey of conformal mapping. Several important aspects had to be omitted, e.g. numerical methods (see e.g.

Studies of the Behavior of the Mapping Function on the Boundary in Conformal Mapping

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Publisher :
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Studies of the Behavior of the Mapping Function on the Boundary in Conformal Mapping by : James Edgar Thompson

Download or read book Studies of the Behavior of the Mapping Function on the Boundary in Conformal Mapping written by James Edgar Thompson and published by . This book was released on 1951 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Mapping

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Author :
Publisher : Courier Corporation
ISBN 13 : 0486150747
Total Pages : 628 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Conformal Mapping by : Roland Schinzinger

Download or read book Conformal Mapping written by Roland Schinzinger and published by Courier Corporation. This book was released on 2012-04-30 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with a brief survey of some basic mathematical concepts, this graduate-level text proceeds to discussions of a selection of mapping functions, numerical methods and mathematical models, nonplanar fields and nonuniform media, static fields in electricity and magnetism, and transmission lines and waveguides. Other topics include vibrating membranes and acoustics, transverse vibrations and buckling of plates, stresses and strains in an elastic medium, steady state heat conduction in doubly connected regions, transient heat transfer in isotropic and anisotropic media, and fluid flow. Revision of 1991 ed. 247 figures. 38 tables. Appendices.

Handbook of Conformal Mappings and Applications

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Publisher : CRC Press
ISBN 13 : 1351718738
Total Pages : 943 pages
Book Rating : 4.3/5 (517 download)

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Book Synopsis Handbook of Conformal Mappings and Applications by : Prem K. Kythe

Download or read book Handbook of Conformal Mappings and Applications written by Prem K. Kythe and published by CRC Press. This book was released on 2019-03-04 with total page 943 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Cauchy Transform, Potential Theory and Conformal Mapping

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Publisher : CRC Press
ISBN 13 : 1498727212
Total Pages : 221 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis The Cauchy Transform, Potential Theory and Conformal Mapping by : Steven R. Bell

Download or read book The Cauchy Transform, Potential Theory and Conformal Mapping written by Steven R. Bell and published by CRC Press. This book was released on 2015-11-04 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cauchy Transform, Potential Theory and Conformal Mapping explores the most central result in all of classical function theory, the Cauchy integral formula, in a new and novel way based on an advance made by Kerzman and Stein in 1976.The book provides a fast track to understanding the Riemann Mapping Theorem. The Dirichlet and Neumann problems f

A Conformal Mapping Technique for Infinitely Connected Regions

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Publisher : American Mathematical Soc.
ISBN 13 : 0821812912
Total Pages : 60 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Conformal Mapping Technique for Infinitely Connected Regions by : Maynard G. Arsove

Download or read book A Conformal Mapping Technique for Infinitely Connected Regions written by Maynard G. Arsove and published by American Mathematical Soc.. This book was released on 1970 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of classical analysis devised originally for the disc are here extended to more general plane regions by the use of Green's lines, the Green's mapping, and an ideal boundary structure generalizing the prime-end structure of Carathéodory. The regions admitted include all bounded finitely connected regions, as well as a broad class of infinitely connected regions. Since certain modifications in the Brelot-Choquet theory are needed to allow for singular Green's lines, an independent development of the theory of Green's lines is given, based on properties of the Green's mapping. These techniques make possible the introduction of a generalized Poisson kernel and integral defined in terms of Green's lines.

Conformal Mapping

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Publisher :
ISBN 13 :
Total Pages : 416 pages
Book Rating : 4.:/5 (42 download)

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Book Synopsis Conformal Mapping by : Zeev Nehari

Download or read book Conformal Mapping written by Zeev Nehari and published by . This book was released on 1952 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Conformal Mapping with Computer-Aided Visualization

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Publisher : CRC Press
ISBN 13 : 9780849389368
Total Pages : 372 pages
Book Rating : 4.3/5 (893 download)

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Book Synopsis Handbook of Conformal Mapping with Computer-Aided Visualization by : Valentin I. Ivanov

Download or read book Handbook of Conformal Mapping with Computer-Aided Visualization written by Valentin I. Ivanov and published by CRC Press. This book was released on 1994-12-16 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Boundary Behaviour of Conformal Maps

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Publisher :
ISBN 13 : 9783527547517
Total Pages : pages
Book Rating : 4.5/5 (475 download)

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Book Synopsis Boundary Behaviour of Conformal Maps by : C. Pommerenke

Download or read book Boundary Behaviour of Conformal Maps written by C. Pommerenke and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Mapping

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821821059
Total Pages : 242 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Conformal Mapping by : Ludwig Bieberbach

Download or read book Conformal Mapping written by Ludwig Bieberbach and published by American Mathematical Soc.. This book was released on 2000 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translated from the fourth German edition by F. Steinhardt, with an expanded Bibliography.

Applied and Computational Complex Analysis, Volume 3

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Publisher : John Wiley & Sons
ISBN 13 : 9780471589860
Total Pages : 660 pages
Book Rating : 4.5/5 (898 download)

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Book Synopsis Applied and Computational Complex Analysis, Volume 3 by : Peter Henrici

Download or read book Applied and Computational Complex Analysis, Volume 3 written by Peter Henrici and published by John Wiley & Sons. This book was released on 1993-04-16 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.

The Cauchy Transform, Potential Theory and Conformal Mapping

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Publisher : CRC Press
ISBN 13 : 9780849382703
Total Pages : 164 pages
Book Rating : 4.3/5 (827 download)

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Book Synopsis The Cauchy Transform, Potential Theory and Conformal Mapping by : Steven R. Bell

Download or read book The Cauchy Transform, Potential Theory and Conformal Mapping written by Steven R. Bell and published by CRC Press. This book was released on 1992-08-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cauchy integral formula is the most central result in all of classical function theory. A recent discovery of Kerzman and Stein allows more theorems than ever to be deduced from simple facts about the Cauchy integral. In this book, the Riemann Mapping Theorem is deduced, the Dirichlet and Neumann problems for the Laplace operator are solved, the Poisson kernal is constructed, and the inhomogenous Cauchy-Reimann equations are solved concretely using formulas stemming from the Kerzman-Stein result. These explicit formulas yield new numerical methods for computing the classical objects of potential theory and conformal mapping, and the book provides succinct, complete explanations of these methods. The Cauchy Transform, Potential Theory, and Conformal Mapping is suitable for pure and applied math students taking a beginning graduate-level topics course on aspects of complex analysis. It will also be useful to physicists and engineers interested in a clear exposition on a fundamental topic of complex analysis, methods, and their application.

Numerical Conformal Mapping

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Publisher : World Scientific
ISBN 13 : 9814289531
Total Pages : 242 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Numerical Conformal Mapping by : Nicolas Papamichael

Download or read book Numerical Conformal Mapping written by Nicolas Papamichael and published by World Scientific. This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique monograph on numerical conformal mapping that gives a comprehensive account of the theoretical, computational and application aspects of the problems of determining conformal modules of quadrilaterals and of mapping conformally onto a rectangle. It contains a detailed study of the theory and application of a domain decomposition method for computing the modules and associated conformal mappings of elongated quadrilaterals, of the type that occur in engineering applications. The reader will find a highly useful and up-to-date survey of available numerical methods and associated computer software for conformal mapping. The book also highlights the crucial role that function theory plays in the development of numerical conformal mapping methods, and illustrates the theoretical insight that can be gained from the results of numerical experiments.This is a valuable resource for mathematicians, who are interested in numerical conformal mapping and wish to study some of the recent developments in the subject, and for engineers and scientists who use, or would like to use, conformal transformations and wish to find out more about the capabilities of modern numerical conformal mapping.

Construction and Applications of Conformal Maps

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Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Construction and Applications of Conformal Maps by : Institute for Numerical Analysis (U.S.)

Download or read book Construction and Applications of Conformal Maps written by Institute for Numerical Analysis (U.S.) and published by . This book was released on 1952 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Maps And Geometry

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Publisher : World Scientific
ISBN 13 : 178634615X
Total Pages : 240 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Conformal Maps And Geometry by : Dmitry Beliaev

Download or read book Conformal Maps And Geometry written by Dmitry Beliaev and published by World Scientific. This book was released on 2019-11-19 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'I very much enjoyed reading this book … Each chapter comes with well thought-out exercises, solutions to which are given at the end of the chapter. Conformal Maps and Geometry presents key topics in geometric function theory and the theory of univalent functions, and also prepares the reader to progress to study the SLE. It succeeds admirably on both counts.'MathSciNetGeometric function theory is one of the most interesting parts of complex analysis, an area that has become increasingly relevant as a key feature in the theory of Schramm-Loewner evolution.Though Riemann mapping theorem is frequently explored, there are few texts that discuss general theory of univalent maps, conformal invariants, and Loewner evolution. This textbook provides an accessible foundation of the theory of conformal maps and their connections with geometry.It offers a unique view of the field, as it is one of the first to discuss general theory of univalent maps at a graduate level, while introducing more complex theories of conformal invariants and extremal lengths. Conformal Maps and Geometry is an ideal resource for graduate courses in Complex Analysis or as an analytic prerequisite to study the theory of Schramm-Loewner evolution.

Conformal Mapping

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Publisher : Courier Corporation
ISBN 13 : 0486145034
Total Pages : 418 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Conformal Mapping by : Zeev Nehari

Download or read book Conformal Mapping written by Zeev Nehari and published by Courier Corporation. This book was released on 2012-05-23 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal mapping is a field in which pure and applied mathematics are both involved. This book tries to bridge the gulf that many times divides these two disciplines by combining the theoretical and practical approaches to the subject. It will interest the pure mathematician, engineer, physicist, and applied mathematician. The potential theory and complex function theory necessary for a full treatment of conformal mapping are developed in the first four chapters, so the reader needs no other text on complex variables. These chapters cover harmonic functions, analytic functions, the complex integral calculus, and families of analytic functions. Included here are discussions of Green's formula, the Poisson formula, the Cauchy-Riemann equations, Cauchy's theorem, the Laurent series, and the Residue theorem. The final three chapters consider in detail conformal mapping of simply-connected domains, mapping properties of special functions, and conformal mapping of multiply-connected domains. The coverage here includes such topics as the Schwarz lemma, the Riemann mapping theorem, the Schwarz-Christoffel formula, univalent functions, the kernel function, elliptic functions, univalent functions, the kernel function, elliptic functions, the Schwarzian s-functions, canonical domains, and bounded functions. There are many problems and exercises, making the book useful for both self-study and classroom use. The author, former professor of mathematics at Carnegie-Mellon University, has designed the book as a semester's introduction to functions of a complex variable followed by a one-year graduate course in conformal mapping. The material is presented simply and clearly, and the only prerequisite is a good working knowledge of advanced calculus.

Experiments in the Computation of Conformal Maps

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Publisher :
ISBN 13 :
Total Pages : 76 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Experiments in the Computation of Conformal Maps by : John Todd

Download or read book Experiments in the Computation of Conformal Maps written by John Todd and published by . This book was released on 1955 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: