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Computational Conformal Mapping

Author : Prem Kythe

Publisher : Springer Science & Business Media

Page : 488 pages

File Size : 50,16 MB

Release : 1998-12-08

Category : Mathematics

ISBN :

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Book Description

A textbook for a graduate class or for self-study by students of applied mathematics and engineering. Assumes at least a first course in complex analysis with emphasis on conformal mapping and Schwarz- Christoffel transformation, a first course in numerical analysis, a solid working competence with the Mathematica software, and some additional knowledge of programming languages. Introduces the theory and computation of conformal mappings of regions that are connected, simply or multiply, onto the unit disk or canonical regions in order to solve boundary value problems. Annotation copyrighted by Book News, Inc., Portland, OR



The Cauchy Transform, Potential Theory and Conformal Mapping

Author : Steven R. Bell

Publisher : CRC Press

Page : 221 pages

File Size : 32,71 MB

Release : 2015-11-04

Category : Mathematics

ISBN : 1498727212

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Book Description

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



Numerical Conformal Mapping

Author : Nicolas Papamichael

Publisher : World Scientific

Page : 242 pages

File Size : 37,89 MB

Release : 2010

Category : Mathematics

ISBN : 9814289531

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Book Description

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.



Inversion Theory and Conformal Mapping

Author : David E. Blair

Publisher : American Mathematical Soc.

Page : 130 pages

File Size : 40,9 MB

Release : 2000-08-17

Category : Mathematics

ISBN : 0821826360

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Book Description

It is rarely taught in an undergraduate or even graduate curriculum that the only conformal maps in Euclidean space of dimension greater than two are those generated by similarities and inversions in spheres. This is in stark contrast to the wealth of conformal maps in the plane. The principal aim of this text is to give a treatment of this paucity of conformal maps in higher dimensions. The exposition includes both an analytic proof in general dimension and a differential-geometric proof in dimension three. For completeness, enough complex analysis is developed to prove the abundance of conformal maps in the plane. In addition, the book develops inversion theory as a subject, along with the auxiliary theme of circle-preserving maps. A particular feature is the inclusion of a paper by Caratheodory with the remarkable result that any circle-preserving transformation is necessarily a Mobius transformation, not even the continuity of the transformation is assumed. The text is at the level of advanced undergraduates and is suitable for a capstone course, topics course, senior seminar or independent study. Students and readers with university courses in differential geometry or complex analysis bring with them background to build on, but such courses are not essential prerequisites.



Conformal Field Theory and Solvable Lattice Models

Author : M Jimbo

Publisher : Elsevier

Page : 439 pages

File Size : 11,47 MB

Release : 2012-12-02

Category : Science

ISBN : 0323150357

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Book Description

Advanced Studies in Pure Mathematics, 16: Conformal Field Theory and Solvable Lattice Models contains nine papers based on the symposium "Conformal field theory and solvable lattice models" held at RIMS, Kyoto, May 1986. These papers cover the following active areas in mathematical physics: conformal field theory, solvable lattice models, affine and Virasoro algebra, and KP equations. The volume begins with an analysis of 1 and 2 point correlation functions of the Gibbs measure of random matrices. This is followed by separate chapters on solvable solid-on-solid (SOS) models; lectures on conformal field theory; the construction of Fermion variables for the 3D Ising Model; and vertex operator construction of null fields (singular vertex operators) based on the oscillator representation of conformal and superconformal algebras with central charge extention. Subsequent chapters deal with Hecke algebra representations of braid groups and classical Yang-Baxter equations; the relationship between the conformal field theories and the soliton equations (KdV, MKdV and Sine-Gordon, etc.) at both quantum and classical levels; and a supersymmetric extension of the Kadomtsev-Petviashvili hierarchy.



Conformal Mapping

Author : Roland Schinzinger

Publisher : Courier Corporation

Page : 628 pages

File Size : 23,28 MB

Release : 2012-04-30

Category : Mathematics

ISBN : 0486150747

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Book Description

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.



Lectures on Quasiconformal Mappings

Author : Lars Valerian Ahlfors

Publisher : American Mathematical Soc.

Page : 178 pages

File Size : 20,66 MB

Release : 2006-07-14

Category : Mathematics

ISBN : 0821836447

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Book Description

Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.



A Mathematical Introduction to Conformal Field Theory

Author : Martin Schottenloher

Publisher : Springer Science & Business Media

Page : 153 pages

File Size : 27,70 MB

Release : 2008-09-15

Category : Science

ISBN : 3540706909

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Book Description

Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The conformal groups are determined and the appearence of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. Part II surveys more advanced topics of conformal field theory such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.



Conformal Maps And Geometry

Author : Dmitry Beliaev

Publisher : World Scientific

Page : 240 pages

File Size : 19,81 MB

Release : 2019-11-19

Category : Mathematics

ISBN : 178634615X

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Book Description

'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 Field Theory and Topology

Author : Toshitake Kohno

Publisher : American Mathematical Soc.

Page : 188 pages

File Size : 19,94 MB

Release : 2002

Category : Mathematics

ISBN : 9780821821305

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Book Description

Geometry and physics have been developed with a strong influence on each other. One of the most remarkable interactions between geometry and physics since 1980 has been an application of quantum field theory to topology and differential geometry. This book focuses on a relationship between two-dimensional quantum field theory and three-dimensional topology which has been studied intensively since the discovery of the Jones polynomial in the middle of the 1980s and Witten's invariantfor 3-manifolds derived from Chern-Simons gauge theory. An essential difficulty in quantum field theory comes from infinite-dimensional freedom of a system. Techniques dealing with such infinite-dimensional objects developed in the framework of quantum field theory have been influential in geometryas well. This book gives an accessible treatment for a rigorous construction of topological invariants originally defined as partition functions of fields on manifolds. The book is organized as follows: The Introduction starts from classical mechanics and explains basic background materials in quantum field theory and geometry. Chapter 1 presents conformal field theory based on the geometry of loop groups. Chapter 2 deals with the holonomy of conformal field theory. Chapter 3 treatsChern-Simons perturbation theory. The final chapter discusses topological invariants for 3-manifolds derived from Chern-Simons perturbation theory.