Complex Potential Theory
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Potential Theory In The Complex Plane
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Author : Thomas Ransford
language : en
Publisher: Cambridge University Press
Release Date : 1995-03-16
Potential Theory In The Complex Plane written by Thomas Ransford and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-16 with Mathematics categories.
Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.
Complex Manifolds Without Potential Theory
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Author : Shiing-shen Chern
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Complex Manifolds Without Potential Theory written by Shiing-shen Chern and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress.... The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#
Complex Potential Theory
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Author : Paul M. Gauthier
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complex Potential Theory written by Paul M. Gauthier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Proceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures, Montréal, Canada, July 26--August 6, 1993
Classical Fine Potential Theory
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Author : Mohamed El Kadiri
language : en
Publisher: Springer Nature
Release Date : 2025-04-03
Classical Fine Potential Theory written by Mohamed El Kadiri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-03 with Mathematics categories.
This comprehensive book explores the intricate realm of fine potential theory. Delving into the real theory, it navigates through harmonic and subharmonic functions, addressing the famed Dirichlet problem within finely open sets of R^n. These sets are defined relative to the coarsest topology on R^n, ensuring the continuity of all subharmonic functions. This theory underwent extensive scrutiny starting from the 1970s, particularly by Fuglede, within the classical or axiomatic framework of harmonic functions. The use of methods from fine potential theory has led to solutions of important classical problems and has allowed the discovery of elegant results for extension of classical holomorphic function to wider classes of “domains”. Moreover, this book extends its reach to the notion of plurisubharmonic and holomorphic functions within plurifinely open sets of C^n and its applications to pluripotential theory. These open sets are defined by coarsest topology that renders all plurisubharmonic functions continuous on C^n. The presentation is meticulously crafted to be largely self-contained, ensuring accessibility for readers at various levels of familiarity with the subject matter. Whether delving into the fundamentals or seeking advanced insights, this book is an indispensable reference for anyone intrigued by potential theory and its myriad applications. Organized into five chapters, the first four unravel the intricacies of fine potential theory, while the fifth chapter delves into plurifine pluripotential theory.
Classical Potential Theory
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Author : David H. Armitage
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Potential Theory written by David H. Armitage and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From its origins in Newtonian physics, potential theory has developed into a major field of mathematical research. This book provides a comprehensive treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, potentials and capacity, the Dirichlet problem and boundary integral representations. The first six chapters deal concretely with the basic theory, and include exercises. The final three chapters are more advanced and treat topological ideas specifically created for potential theory, such as the fine topology, the Martin boundary and minimal thinness. The presentation is largely self-contained and is accessible to graduate students, the only prerequisites being a reasonable grounding in analysis and several variables calculus, and a first course in measure theory. The book will prove an essential reference to all those with an interest in potential theory and its applications.
The Cauchy Transform Potential Theory And Conformal Mapping
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Author : Steven R. Bell
language : en
Publisher: CRC Press
Release Date : 1992-08-14
The Cauchy Transform Potential Theory And Conformal Mapping written by Steven R. Bell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-14 with Mathematics categories.
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.
Function Spaces And Potential Theory
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Author : David R. Adams
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-11-22
Function Spaces And Potential Theory written by David R. Adams and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-22 with Mathematics categories.
"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society
Complex Variables With Applications
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Author : Saminathan Ponnusamy
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-26
Complex Variables With Applications written by Saminathan Ponnusamy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-26 with Mathematics categories.
Explores the interrelations between real and complex numbers by adopting both generalization and specialization methods to move between them, while simultaneously examining their analytic and geometric characteristics Engaging exposition with discussions, remarks, questions, and exercises to motivate understanding and critical thinking skills Encludes numerous examples and applications relevant to science and engineering students
Foundations Of Potential Theory
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Author : Oliver Dimon Kellogg
language : en
Publisher: Courier Corporation
Release Date : 1953-01-01
Foundations Of Potential Theory written by Oliver Dimon Kellogg and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953-01-01 with Science categories.
Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.
Theoretical Fluid Dynamics
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Author : Achim Feldmeier
language : en
Publisher: Springer Nature
Release Date : 2020-03-17
Theoretical Fluid Dynamics written by Achim Feldmeier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-17 with Science categories.
This textbook gives an introduction to fluid dynamics based on flows for which analytical solutions exist, like individual vortices, vortex streets, vortex sheets, accretions disks, wakes, jets, cavities, shallow water waves, bores, tides, linear and non-linear free-surface waves, capillary waves, internal gravity waves and shocks. Advanced mathematical techniques ("calculus") are introduced and applied to obtain these solutions, mostly from complex function theory (Schwarz-Christoffel theorem and Wiener-Hopf technique), exterior calculus, singularity theory, asymptotic analysis, the theory of linear and nonlinear integral equations and the theory of characteristics. Many of the derivations, so far contained only in research journals, are made available here to a wider public.