Oliver Dimon Kellogg

Foundations of Potential Theory by Oliver Dimon Kellogg is a comprehensive and authoritative text on the mathematical theory of potentials. The book covers the fundamental concepts and principles of potential theory, including the Laplace equation, harmonic functions, Green's functions, and the maximum principle. It also explores the applications of potential theory in various fields, such as electrostatics, magnetostatics, fluid mechanics, and elasticity. The book is divided into three parts. Part I introduces the basic concepts and principles of potential theory, including the Laplace equation and its solutions, harmonic functions, and Green's functions. Part II explores the applications of potential theory in electrostatics, magnetostatics, and fluid mechanics. Part III covers more advanced topics, such as the Dirichlet problem, the Neumann problem, and the Riemann mapping theorem. Throughout the book, Kellogg provides clear and concise explanations of the mathematical concepts and their applications. The text is also richly illustrated with diagrams and figures to help readers visualize the concepts and principles. Foundations of Potential Theory is an essential reference for mathematicians, physicists, and engineers who work in the fields of potential theory, electrostatics, magnetostatics, fluid mechanics, and elasticity. It is also an excellent textbook for graduate students studying these subjects. This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

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 by Oliver Dimon Kellogg is a comprehensive and authoritative text on the mathematical theory of potentials. The book covers the fundamental concepts and principles of potential theory, including the Laplace equation, Green's function, boundary value problems, and harmonic functions. The author provides a detailed treatment of the mathematical techniques used in potential theory, including complex analysis, functional analysis, and measure theory. The book also includes numerous examples and exercises that illustrate the theory and its applications. This classic text is an essential reference for mathematicians, physicists, and engineers interested in potential theory and its applications. This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

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.