Foundations Of Potential Theory
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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.
Foundations Of Potential Theory
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Author : Oliver Dimon Kellogg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Foundations Of Potential Theory written by Oliver Dimon Kellogg 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 2013-11-11 with Mathematics categories.
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
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Author : O D (Oliver Dimon) B 1878 Kellogg
language : en
Publisher: Hassell Street Press
Release Date : 2021-09-09
Foundations Of Potential Theory written by O D (Oliver Dimon) B 1878 Kellogg and has been published by Hassell Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with categories.
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Foundations Of Potential Theory
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Author : Oliver D. Kellogg
language : en
Publisher:
Release Date : 1920
Foundations Of Potential Theory written by Oliver D. Kellogg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1920 with categories.
Foundations Of Potential Theory
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Author : Kellogg Oliver Dimon
language : en
Publisher: Barman Press
Release Date : 2007-03-01
Foundations Of Potential Theory written by Kellogg Oliver Dimon and has been published by Barman Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-01 with Philosophy categories.
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 Potential Theory By Oliver Dimon Kellogg With 30 Figures
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Author : Oliver Dimon Kellogg
language : en
Publisher:
Release Date : 1929
Foundations Of Potential Theory By Oliver Dimon Kellogg With 30 Figures written by Oliver Dimon Kellogg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1929 with categories.
Foundations Of Modern Potential Theory
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Author : Naum S. Landkof
language : en
Publisher: Springer
Release Date : 2011-11-15
Foundations Of Modern Potential Theory written by Naum S. Landkof and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-15 with Mathematics categories.
For a long time potential theory was necessarily viewed as only another chapter of mathematical physics. Developing in close connection with the theory of boundary-value problems for the Laplace operator, it led to the creation of the mathematical apparatus of potentials of single and double layers; this was adequate for treating problems involving smooth boundaries. A. M. Lyapunov is to be credited with the rigorous analysis of the properties of potentials and the possibilities for applying them to the 1 solution of boundary-value problems. The results he obtained at the end of the 19th century later received a more detailed and sharpened exposition in the book by N. M. Gunter, published in Paris in 1934 and 2 in New York 1967 with additions and revisions. Of fundamental significance to potential theory also was the work of H. Poincare, especially his method of sweeping out mass (balayage). At the beginning of the 20th century the work of S. Zaremba and especially of H. Lebesgue attracted the attention of mathematicians to the unsolvable cases of the classical Dirichlet problem. Through the efforts of O. Kellogg, G. Bouligand, and primarily N. Wiener, by the middle of the 20th century the problem of characterizing the so-called irregular points of the boundary of a region (i. e. the points at which the continuity of the solution of the Dirichlet problem may be violated) was completely solved and a procedure to obtain a generalized solution to the Dirichlet problem was described.
Foundations Of Modern Potential Theory
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Author : Naum Samoĭlovich Landkof
language : en
Publisher: Springer
Release Date : 1972
Foundations Of Modern Potential Theory written by Naum Samoĭlovich Landkof and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
Potential Theory In Gravity And Magnetic Applications
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Author : Richard J. Blakely
language : en
Publisher: Cambridge University Press
Release Date : 1996-09-13
Potential Theory In Gravity And Magnetic Applications written by Richard J. Blakely 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 1996-09-13 with Mathematics categories.
This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The theory is then applied to the interpretation of gravity and magnetic anomalies, drawing on examples from modern geophysical literature. Topics explored include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book includes numerous exercises and a variety of computer subroutines written in FORTRAN. Graduate students and researchers in geophysics will find this book essential.
Nonlinear Potential Theory And Weighted Sobolev Spaces
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Author : Bengt O. Turesson
language : en
Publisher: Springer
Release Date : 2007-05-06
Nonlinear Potential Theory And Weighted Sobolev Spaces written by Bengt O. Turesson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.