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Conformal Representation
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Book Synopsis Conformal Representation by : Constantin Caratheodory
Download or read book Conformal Representation written by Constantin Caratheodory and published by Courier Corporation. This book was released on 1998-01-01 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction discusses the Möbius transformation, non-Euclidean geometry, elementary transformations, Schwarz's Lemma, transformation of the frontier and closed surfaces, and the general theorem of uniformization. Detailed proofs.
Book Synopsis On the Conformal Representation of Plane Curves by : Charlotte Elvira Pengra
Download or read book On the Conformal Representation of Plane Curves written by Charlotte Elvira Pengra and published by . This book was released on 1904 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Conformal Representation by : Leo Lewent
Download or read book Conformal Representation written by Leo Lewent and published by . This book was released on 1925 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Studies in Conformal Representation by : Clarence Keyser
Download or read book Studies in Conformal Representation written by Clarence Keyser and published by . This book was released on 1911 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Kernel Function and Conformal Mapping by : Stefan Bergman
Download or read book The Kernel Function and Conformal Mapping written by Stefan Bergman and published by American Mathematical Soc.. This book was released on 1950 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of ""The Kernel Function"". The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, physicists, and computer scientists. The applications of orthogonal functions in solving boundary value problems and conformal mappings onto canonical domains are discussed; and publications are indicated where programs for carrying out numerical work using high-speed computers can be found.The unification of methods in the theory of functions of one and several complex variables is one of the purposes of introducing the kernel function and the domains with a distinguished boundary. This approach has been extensively developed during the last two decades. This second edition of Professor Bergman's book reviews this branch of the theory including recent developments not dealt with in the first edition. The presentation of the topics is simple and presupposes only knowledge of an elementary course in the theory of analytic functions of one variable.
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.
Book Synopsis Univalent Functions and Conformal Mapping by : James A. Jenkins
Download or read book Univalent Functions and Conformal Mapping written by James A. Jenkins and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with the application of the method of the extremal metric to the theory of univalent functions. Apart from an introductory chapter in which a brief survey of the development of this theory is given there is therefore no attempt to follow up other methods of treatment. Nevertheless such is the power of the present method that it is possible to include the great majority of known results on univalent functions. It should be mentioned also that the discussion of the method of the extremal metric is directed toward its application to univalent functions, there being no space to present its numerous other applications, particularly to questions of quasiconformal mapping. Also it should be said that there has been no attempt to provide an exhaustive biblio graphy, reference normally being confined to those sources actually quoted in the text. The central theme of our work is the General Coefficient Theorem which contains as special cases a great many of the known results on univalent functions. In a final chapter we give also a number of appli cations of the method of symmetrization. At the time of writing of this monograph the author has been re ceiving support from the National Science Foundation for which he wishes to express his gratitude. His thanks are due also to Sister BARBARA ANN Foos for the use of notes taken at the author's lectures in Geo metric Function Theory at the University of Notre Dame in 1955-1956.
Book Synopsis Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces by : R. Courant
Download or read book Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces written by R. Courant and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has always been a temptation for mathematicians to present the crystallized product of their thoughts as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods of more general significance. The present book deals with subjects of this category. It is written in a style which, as the author hopes, expresses adequately the balance and tension between the individuality of mathematical objects and the generality of mathematical methods. The author has been interested in Dirichlet's Principle and its various applications since his days as a student under David Hilbert. Plans for writing a book on these topics were revived when Jesse Douglas' work suggested to him a close connection between Dirichlet's Principle and basic problems concerning minimal sur faces. But war work and other duties intervened; even now, after much delay, the book appears in a much less polished and complete form than the author would have liked."
Book Synopsis Computational Conformal Mapping by : Prem Kythe
Download or read book Computational Conformal Mapping written by Prem Kythe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book evolved out of a graduate course given at the University of New Orleans in 1997. The class consisted of students from applied mathematics andengineering. Theyhadthebackgroundofatleastafirstcourseincomplex analysiswithemphasisonconformalmappingandSchwarz-Christoffeltrans formation, a firstcourse in numerical analysis, and good to excellent working knowledgeofMathematica* withadditionalknowledgeofsomeprogramming languages. Sincetheclasshad nobackground inIntegralEquations, thechap tersinvolvingintegralequationformulations werenotcoveredindetail, except for Symm's integral equation which appealed to a subsetofstudents who had some training in boundary element methods. Mathematica was mostly used for computations. In fact, it simplified numerical integration and other oper ations very significantly, which would have otherwise involved programming inFortran, C, orotherlanguageofchoice, ifclassical numericalmethods were attempted. Overview Exact solutions of boundary value problems for simple regions, such as cir cles, squares or annuli, can be determined with relative ease even where the boundaryconditionsarerathercomplicated. Green'sfunctionsforsuchsimple regions are known. However, for regions with complex structure the solution ofa boundary value problem often becomes more difficult, even for a simple problemsuchastheDirichletproblem. Oneapproachtosolvingthesedifficult problems is to conformally transform a given multiply connected region onto *Mathematica is a registered trade mark of Wolfram Research, Inc. ix x PREFACE simpler canonical regions. This will, however, result in change not only in the region and the associated boundary conditions but also in the governing differential equation. As compared to the simply connected regions, confor mal mapping ofmultiply connected regions suffers from severe limitations, one of which is the fact that equal connectivity ofregions is not a sufficient condition to effect a reciprocally connected map ofone region onto another.
Book Synopsis The Conformal Transformation of an Airfoil Into a Straight Line and Its Application to the Inverse Problem of Airfoil Theory by : William Mutterperl
Download or read book The Conformal Transformation of an Airfoil Into a Straight Line and Its Application to the Inverse Problem of Airfoil Theory written by William Mutterperl and published by . This book was released on 1944 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summary: A method of conformal transformation is developed that maps an airfoil into a straight line, the line being chosen as the extended chord line of the airfoil. The mapping is accomplished by operating directly with the airfoil ordinates. The absence of any preliminary transformation is found to shorten the work substantially over that of previous methods. Use is made of the superposition of solutions to obtain a rigorous counterpart of the approximate methods of thin-airfoil theory. The method is applied to the solution of the direct and inverse problems for arbitrary airfoils and pressure distributions. Numerical examples are given. Applications to more general types of regions, in particular to biplanes and to cascades of airfoils, are indicated.
Download or read book conformal repreesentation written by and published by CUP Archive. This book was released on with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Conformal Representation by : Ruth Hieger
Download or read book Conformal Representation written by Ruth Hieger and published by . This book was released on 1916 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Mathematical Introduction to Conformal Field Theory by : Martin Schottenloher
Download or read book A Mathematical Introduction to Conformal Field Theory written by Martin Schottenloher and published by Springer Science & Business Media. This book was released on 2008-09-15 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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:
Book Synopsis Conformal Field Theory and Topology by : Toshitake Kohno
Download or read book Conformal Field Theory and Topology written by Toshitake Kohno and published by American Mathematical Soc.. This book was released on 2002 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Gravity and Cosmology Based on Conformal Field Theory by : Ken-ji Hamada
Download or read book Quantum Gravity and Cosmology Based on Conformal Field Theory written by Ken-ji Hamada and published by Cambridge Scholars Publishing. This book was released on 2019-01-18 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the world beyond the Planck scale that provides the minimum unit of the universe? The goal of quantum gravity is to reveal physical laws in such a world. There, quantum fluctuations of gravity become large, and what is called a background-free world where the concept of time and distance is lost shall be realized. The renormalizable quantum gravity introduced in this book offers a theory in which such a world is described by a certain conformal field theory and a deviation from there is handled as a perturbation. This is the state-of-the-art of modern physics that will help in understanding the history of the universe, from its birth to the present.
