Conformal Mapping

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Author: Ludwig Bieberbach

Publisher: American Mathematical Soc.

ISBN: 0821821059

Category: Mathematics

Page: 234

View: 1305

Translated from the fourth German edition by F. Steinhardt, with an expanded Bibliography.

Handbook of Conformal Mappings and Applications

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Author: Prem K. Kythe

Publisher: CRC Press

ISBN: 135171872X

Category: Mathematics

Page: 906

View: 7076

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.

Advanced Mathematics for Applications

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Author: Andrea Prosperetti

Publisher: Cambridge University Press

ISBN: 1139492683

Category: Mathematics

Page: N.A

View: 3777

The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough presentation.

Complex Analysis

The Geometric Viewpoint

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Author: Steven George Krantz

Publisher: MAA

ISBN: 9780883850350

Category: Mathematics

Page: 219

View: 1720

In this second edition of a Carus Monograph Classic, Steven G. Krantz, a leading worker in complex analysis and a winner of the Chauvenet Prize for outstanding mathematical exposition, develops material on classical non-Euclidean geometry. He shows how it can be developed in a natural way from the invariant geometry of the complex disk. He also introduces the Bergmann kernel and metric and provides profound applications, some of which have never appeared in print before. In general, the new edition represents a considerable polishing and re-thinking of the original successful volume. A minimum of geometric formalism is used to gain a maximum of geometric and analytic insight. The climax of the book is an introduction to several complex variables from the geometric viewpoint. Poincar's theorem, that the ball and bidisc are biholomorphically inequivalent, is discussed and proved.

Gesammelte mathematische Abhandlungen

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Author: Hermann Amandus Schwarz

Publisher: American Mathematical Soc.

ISBN: 9780828402606

Category: Mathematics

Page: 708

View: 2923

This is the second edition of the collected papers of an important mathematician. His most notable work was in minimal surfaces and conformal mapping (the Schwarz inequality, the Schwarz-Christoffel mapping of a linear polygon, etc.). The text is in German.

Gesammelte Abhandlungen

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Author: Oswald Teichmüller,Lars Valerian Ahlfors,Frederick W. Gehring

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 751

View: 3030

Introduction to Complex Analysis

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Author: Rolf Herman Nevanlinna,Veikko Paatero

Publisher: American Mathematical Soc.

ISBN: 9780821843994

Category: Mathematics

Page: 350

View: 4490

It really is a gem, both in terms of its table of contents and the level of discussion. The exercises also look very good. --Clifford Earle, Cornell University This book has a soul and has passion. --William Abikoff, University of Connecticut This classic book gives an excellent presentation of topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem. The two quotes above confirm that the book can be successfully used as a text for a class or for self-study.

On the Difference Quotient Operator

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Author: Nicholas Anthony Martin

Publisher: Ann Arbor, Mich. : University Microfilms International

ISBN: N.A

Category: Operator theory

Page: 138

View: 7753

Analytic Function Theory

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Author: Einar Hille

Publisher: American Mathematical Soc.

ISBN: 9780821829141

Category: Analytic functions

Page: 496

View: 7845

This famous work is a textbook that emphasizes the conceptual and historical continuity of analytic function theory. The second volume broadens from a textbook to a textbook-treatise, covering the ``canonical'' topics (including elliptic functions, entire and meromorphic functions, as well as conformal mapping, etc.) and other topics nearer the expanding frontier of analytic function theory. In the latter category are the chapters on majorization and on functions holomorphic in a half-plane.

Analytic Function Theory, Volume I

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Author: Einar Hille

Publisher: American Mathematical Soc.

ISBN: 082187568X

Category:

Page: 308

View: 5709

Second Edition. This famous work is a textbook that emphasizes the conceptual and historical continuity of analytic function theory. The second volume broadens from a textbook to a textbook-treatise, covering the "canonical" topics (including elliptic functions, entire and meromorphic functions, as well as conformal mapping, etc.) and other topics nearer the expanding frontier of analytic function theory. In the latter category are the chapters on majorization and on functions holomorphic in a half-plane.

Conformal Invariants

Topics in Geometric Function Theory

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Author: Lars Valerian Ahlfors

Publisher: American Mathematical Soc.

ISBN: 0821852701

Category: Mathematics

Page: 160

View: 6949

Most conformal invariants can be described in terms of extremal properties. Conformal invariants and extremal problems are therefore intimately linked and form together the central theme of this classic book which is primarily intended for students with approximately a year's background in complex variable theory. The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. At the time of the book's original appearance, much of this material had never appeared in book form, particularly the discussion of the theory of extremal length. Schiffer's variational method also receives special attention, and a proof of $\vert a_4\vert \leq 4$ is included which was new at the time of publication. The last two chapters give an introduction to Riemann surfaces, with topological and analytical background supplied to support a proof of the uniformization theorem. Included in this new reprint is a Foreword by Peter Duren, F. W. Gehring, and Brad Osgood, as well as an extensive errata. ... encompasses a wealth of material in a mere one hundred and fifty-one pages. Its purpose is to present an exposition of selected topics in the geometric theory of functions of one complex variable, which in the author's opinion should be known by all prospective workers in complex analysis. From a methodological point of view the approach of the book is dominated by the notion of conformal invariant and concomitantly by extremal considerations. ... It is a splendid offering. --Reviewed for Math Reviews by M. H. Heins in 1975

The Logarithmic Potential and Other Monographs

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Author: Griffith Conrad Evans,Gilbert Ames Bliss,Edward Kasner

Publisher: American Mathematical Soc.

ISBN: 9780828403054

Category: Mathematics

Page: 117

View: 8395

The volume contains the following monographs: The Logarithmic Potential by Evans Fundamental Existence Theorems by Bliss Differential-Geometric Aspects of Dynamics by Kasner All three monographs were originally published by the AMS and are now available in this single volume from AMS Chelsea Publishing.

Automorphic Functions

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Author: Lester R. Ford

Publisher: American Mathematical Soc.

ISBN: 9780821837412

Category: Mathematics

Page: 333

View: 1808

Lester Ford's book was the first treatise in English on automorphic functions. At the time of its publication (1929), it was welcomed for its elegant treatment of groups of linear transformations and for the remarkably clear and explicit exposition throughout the book. Ford's extraordinary talent for writing has been memorialized in the prestigious award that bears his name. The book, in the meantime, has become a recognized classic. Ford's approach is primarily through analytic function theory. The first part of the book covers groups of linear transformations, especially Fuchsian groups, fundamental domains, and functions that are invariant under the groups, including the classical elliptic modular functions and Poincare theta series. The second part of the book covers conformal mappings, uniformization, and connections between automorphic functions and differential equations with regular singular points, such as the hypergeometric equation.

An introduction to complex analysis

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Author: O. Carruth McGehee

Publisher: Wiley-Interscience

ISBN: 9780471332336

Category: Mathematics

Page: 425

View: 6430

* Contains over 100 sophisticated graphics to provide helpful examples and reinforce important concepts