Foundations Of Potential Theory

Author : Oliver Dimon Kellogg
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 45,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783642908507

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Foundations of Potential Theory by Oliver Dimon Kellogg Pdf

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.

Author : Oliver Dimon Kellogg
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642867484

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Foundations of Potential Theory by Oliver Dimon Kellogg Pdf

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.

Author : Oliver D. Kellogg
Publisher : Unknown
Page : 384 pages
File Size : 50,5 Mb
Release : 1950
Category : Electronic
ISBN : OCLC:1106820269

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Foundations of Potential Theory by Oliver D. Kellogg Pdf

Author : Kellogg Oliver Dimon
Publisher : Barman Press
Page : 396 pages
File Size : 41,6 Mb
Release : 2007-03-01
Category : Philosophy
ISBN : 9781406706482

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Foundations of Potential Theory by Kellogg Oliver Dimon Pdf

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.

Author : Naum Samoĭlovich Landkof
Publisher : Springer
Page : 446 pages
File Size : 50,5 Mb
Release : 1972
Category : Functions of complex variables
ISBN : UCAL:B4406641

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Foundations of Modern Potential Theory by Naum Samoĭlovich Landkof Pdf

Author : Wilfried Brauer
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 41,6 Mb
Release : 1997-10-24
Category : Computers
ISBN : 354063746X

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Foundations of Computer Science by Wilfried Brauer Pdf

Content Description #Dedicated to Wilfried Brauer.#Includes bibliographical references and index.

Author : N. S. Landkof
Publisher : Unknown
Page : 0 pages
File Size : 53,9 Mb
Release : 1972
Category : Electronic
ISBN : OCLC:472172029

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Foundations of modern potential theory by N. S. Landkof Pdf

Author : Matthew Baker,Robert S. Rumely
Publisher : American Mathematical Soc.
Page : 466 pages
File Size : 45,8 Mb
Release : 2010-03-10
Category : Mathematics
ISBN : 9780821849248

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Potential Theory and Dynamics on the Berkovich Projective Line by Matthew Baker,Robert S. Rumely Pdf

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.

Author : O D (Oliver Dimon) B 1878 Kellogg
Publisher : Hassell Street Press
Page : 400 pages
File Size : 45,9 Mb
Release : 2021-09-09
Category : Electronic
ISBN : 101406158X

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Foundations of Potential Theory by O D (Oliver Dimon) B 1878 Kellogg Pdf

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.

Author : Olav Kallenberg
Publisher : Springer Science & Business Media
Page : 670 pages
File Size : 52,7 Mb
Release : 2002-01-08
Category : Mathematics
ISBN : 0387953132

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Foundations of Modern Probability by Olav Kallenberg Pdf

The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

Author : Richard J. Blakely
Publisher : Cambridge University Press
Page : 468 pages
File Size : 47,9 Mb
Release : 1996-09-13
Category : Mathematics
ISBN : 0521575478

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Potential Theory in Gravity and Magnetic Applications by Richard J. Blakely Pdf

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.

Author : O. Penrose
Publisher : Elsevier
Page : 272 pages
File Size : 44,7 Mb
Release : 2016-09-21
Category : Science
ISBN : 9781483156484

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Foundations of Statistical Mechanics by O. Penrose Pdf

International Series of Monographs in Natural Philosophy, Volume 22: Foundations of Statistical Mechanics: A Deductive Treatment presents the main approaches to the basic problems of statistical mechanics. This book examines the theory that provides explicit recognition to the limitations on one's powers of observation. Organized into six chapters, this volume begins with an overview of the main physical assumptions and their idealization in the form of postulates. This text then examines the consequences of these postulates that culminate in a derivation of the fundamental formula for calculating probabilities in terms of dynamic quantities. Other chapters provide a careful analysis of the significant notion of entropy, which shows the links between thermodynamics and statistical mechanics and also between communication theory and statistical mechanics. The final chapter deals with the thermodynamic concept of entropy. This book is intended to be suitable for students of theoretical physics. Probability theorists, statisticians, and philosophers will also find this book useful.

Author : Lester La Verne Helms
Publisher : John Wiley & Sons
Page : 314 pages
File Size : 52,7 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:39015036999418

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Introduction to Potential Theory by Lester La Verne Helms Pdf

Author : Herbert S. Green
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642571626

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Information Theory and Quantum Physics by Herbert S. Green Pdf

In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.

Author : Lester L. Helms
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 40,8 Mb
Release : 2014-04-10
Category : Mathematics
ISBN : 9781447164227

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Potential Theory by Lester L. Helms Pdf

Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In this new edition, many exercises have been added to reconnect the subject matter to the physical sciences. This book will undoubtedly be useful to graduate students and researchers in mathematics, physics and engineering.