Foundations Of Potential Theory
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Foundations of Potential Theory
Author | : Oliver Dimon Kellogg |
Publsiher | : Springer Science & Business Media |
Total Pages | : 392 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 9783642908507 |
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The present volume gives a systematic treatment of potential functions. It takes its origin in two courses, one elementary and one advanced, which the author has given at intervals during the last ten years, and has a two-fold purpose: first, to serve as an introduction for students whose attainments in the Calculus include some knowledge of partial derivatives and multiple and line integrals; and secondly, to provide the reader with the fundamentals of the subject, so that he may proceed immediately to the applications, or to the periodical literature of the day. It is inherent in the nature of the subject that physical intuition and illustration be appealed to freely, and this has been done. However, in order that the book may present sound ideals to the student, and also serve the mathematician, both for purposes of reference and as a basis for further developments, the proofs have been given by rigorous methods. This has led, at a number of points, to results either not found elsewhere, or not readily accessible. Thus, Chapter IV contains a proof for the general regular region of the divergence theorem (Gauss', or Green's theorem) on the reduction of volume to surface integrals. The treatment of the fundamental existence theorems in Chapter XI by means of integral equations meets squarely the difficulties incident to the discontinuity of the kernel, and the same chapter gives an account of the most recent developments with respect to the Dirichlet problem.
Foundations of Potential Theory
Author | : Oliver Dimon Kellogg |
Publsiher | : Springer Science & Business Media |
Total Pages | : 395 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9783642867484 |
Download Foundations of Potential Theory Book in PDF, Epub and Kindle
The present volume gives a systematic treatment of potential functions. It takes its origin in two courses, one elementary and one advanced, which the author has given at intervals during the last ten years, and has a two-fold purpose: first, to serve as an introduction for students whose attainments in the Calculus include some knowledge of partial derivatives and multiple and line integrals; and secondly, to provide the reader with the fundamentals of the subject, so that he may proceed immediately to the applications, or to the periodical literature of the day. It is inherent in the nature of the subject that physical intuition and illustration be appealed to freely, and this has been done. However, that the book may present sound ideals to the student, and in order also serve the mathematician, both for purposes of reference and as a basis for further developments, the proofs have been given by rigorous methods. This has led, at a number of points, to results either not found elsewhere, or not readily accessible. Thus, Chapter IV contains a proof for the general regular region of the divergence theorem (Gauss', or Green's theorem) on the reduction of volume to surface integrals. The treatment of the fundamental existence theorems in Chapter XI by means of integral equations meets squarely the difficulties incident to ·the discontinuity of the kernel, and the same chapter gives an account of the most recent developments with respect to the Dirichlet problem.
Foundations of Potential Theory
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Author | : Oliver D. Kellogg |
Publsiher | : Unknown |
Total Pages | : 384 |
Release | : 1950 |
Genre | : Electronic Book |
ISBN | : OCLC:1106820269 |
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Foundations of Potential Theory
Author | : Kellogg Oliver Dimon |
Publsiher | : Barman Press |
Total Pages | : 396 |
Release | : 2007-03-01 |
Genre | : Philosophy |
ISBN | : 9781406706482 |
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Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.
Foundations of Modern Potential Theory
Author | : Naum Samoĭlovich Landkof |
Publsiher | : Springer |
Total Pages | : 446 |
Release | : 1972 |
Genre | : Functions of complex variables |
ISBN | : UCAL:B4406641 |
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Foundations of Computer Science
Author | : Wilfried Brauer |
Publsiher | : Springer Science & Business Media |
Total Pages | : 536 |
Release | : 1997-10-24 |
Genre | : Computers |
ISBN | : 354063746X |
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Content Description #Dedicated to Wilfried Brauer.#Includes bibliographical references and index.
Potential Theory and Dynamics on the Berkovich Projective Line
Author | : Matthew Baker,Robert S. Rumely |
Publsiher | : American Mathematical Soc. |
Total Pages | : 466 |
Release | : 2010-03-10 |
Genre | : Mathematics |
ISBN | : 9780821849248 |
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The purpose of this book is to develop the foundations of potential theory and rational dynamics on the Berkovich projective line over an arbitrary complete, algebraically closed non-Archimedean field. In addition to providing a concrete and ``elementary'' introduction to Berkovich analytic spaces and to potential theory and rational iteration on the Berkovich line, the book contains applications to arithmetic geometry and arithmetic dynamics. A number of results in the book are new, and most have not previously appeared in book form. Three appendices--on analysis, $\mathbb{R}$-trees, and Berkovich's general theory of analytic spaces--are included to make the book as self-contained as possible. The authors first give a detailed description of the topological structure of the Berkovich projective line and then introduce the Hsia kernel, the fundamental kernel for potential theory. Using the theory of metrized graphs, they define a Laplacian operator on the Berkovich line and construct theories of capacities, harmonic and subharmonic functions, and Green's functions, all of which are strikingly similar to their classical complex counterparts. After developing a theory of multiplicities for rational functions, they give applications to non-Archimedean dynamics, including local and global equidistribution theorems, fixed point theorems, and Berkovich space analogues of many fundamental results from the classical Fatou-Julia theory of rational iteration. They illustrate the theory with concrete examples and exposit Rivera-Letelier's results concerning rational dynamics over the field of $p$-adic complex numbers. They also establish Berkovich space versions of arithmetic results such as the Fekete-Szego theorem and Bilu's equidistribution theorem.
Foundations of modern potential theory
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Author | : N. S. Landkof |
Publsiher | : Unknown |
Total Pages | : 0 |
Release | : 1972 |
Genre | : Electronic Book |
ISBN | : OCLC:472172029 |
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