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Author: Oliver Dimon Kellogg
Publisher: Springer Science & Business Media
ISBN: 3642908500
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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
ISBN: 3642908500
Category : Mathematics
Languages : en
Pages : 392
Get Book
Book Description
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 D. Kellogg
Publisher:
ISBN:
Category :
Languages : en
Pages : 384
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Book Description
Author: Oliver Dimon Kellogg
Publisher: Springer Science & Business Media
ISBN: 3642867480
Category : Mathematics
Languages : en
Pages : 395
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Book Description
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: Kellogg Oliver Dimon
Publisher: Barman Press
ISBN: 1406706485
Category : Philosophy
Languages : en
Pages : 396
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Book Description
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
ISBN:
Category : Functions of complex variables
Languages : en
Pages : 446
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Book Description
Author: Matthew Baker
Publisher: American Mathematical Soc.
ISBN: 0821849247
Category : Mathematics
Languages : en
Pages : 466
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Book Description
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: Wilfried Brauer
Publisher: Springer Science & Business Media
ISBN: 9783540637462
Category : Computers
Languages : en
Pages : 536
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Book Description
Content Description #Dedicated to Wilfried Brauer.#Includes bibliographical references and index.
Author: Richard J. Blakely
Publisher: Cambridge University Press
ISBN: 9780521575478
Category : Mathematics
Languages : en
Pages : 468
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Book Description
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
ISBN: 1483156486
Category : Science
Languages : en
Pages : 272
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Book Description
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: Olav Kallenberg
Publisher: Springer Science & Business Media
ISBN: 9780387953137
Category : Mathematics
Languages : en
Pages : 670
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Book Description
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.
