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Author: Constantin Caratheodory
Publisher: Courier Corporation
ISBN: 9780486400280
Category : Mathematics
Languages : en
Pages : 132
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Book Description
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.
Author: Constantin Caratheodory
Publisher: Courier Corporation
ISBN: 9780486400280
Category : Mathematics
Languages : en
Pages : 132
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Book Description
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.
Author: Leo Lewent
Publisher:
ISBN:
Category : Conformal mapping
Languages : en
Pages : 176
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Book Description
Author: Clarence Keyser
Publisher:
ISBN:
Category :
Languages : en
Pages : 84
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Book Description
Author: Zeev Nehari
Publisher: Courier Corporation
ISBN: 0486145034
Category : Mathematics
Languages : en
Pages : 418
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Book Description
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.
Author: Ruth Hieger
Publisher:
ISBN:
Category :
Languages : en
Pages : 226
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Book Description
Author: Charlotte Elvira Pengra
Publisher:
ISBN:
Category : Conformal mapping
Languages : en
Pages : 26
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Book Description
Author:
Publisher: CUP Archive
ISBN:
Category :
Languages : en
Pages : 120
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Book Description
Author: Stefan Bergman
Publisher: American Mathematical Soc.
ISBN: 0821815059
Category : Mathematics
Languages : en
Pages : 269
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Book Description
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.
Author: George Arthur Chaney
Publisher:
ISBN:
Category :
Languages : en
Pages : 80
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Book Description
Author: Martin Schottenloher
Publisher: Springer Science & Business Media
ISBN: 3540706909
Category : Science
Languages : en
Pages : 153
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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.
