Foundations of Potential Theory

Oliver Dimon Kellogg

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English

Springer-Verlag Berlin and Heidelberg GmbH & Co. K
15 April 2012

Mathematics & Sciences; Calculus & mathematical analysis; Mathematical physics

Series: Grundlehren der mathematischen Wissenschaften

Summary
Details

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.

By: Oliver Dimon Kellogg
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Edition: Softcover reprint of the original 1st ed. 1967
Volume: 31
Dimensions: Height: 235mm, Width: 155mm, Spine: 20mm
Weight: 604g
ISBN: 9783642867507
ISBN 10: 3642867502
Series: Grundlehren der mathematischen Wissenschaften
Pages: 386
Publication Date: 15 April 2012
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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Foundations of Potential Theory

Oliver Dimon Kellogg

$138.95

Paperback

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