Download PDF Foundations of Potential Theory, by Oliver Dimon Kellogg
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Foundations of Potential Theory, by Oliver Dimon Kellogg
Download PDF Foundations of Potential Theory, by Oliver Dimon Kellogg
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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.
- Published on: 2013-01-26
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x .82" w x 5.98" l, 1.17 pounds
- Binding: Paperback
- 398 pages
Most helpful customer reviews
21 of 21 people found the following review helpful.
THE book on classical potential theory
By John Robbins
There are few books left in print on this captivating subject from theoretical mechanics. Kellogg's presentation is clear and mathematically formal. This is an excellent reprint from Dover.
Now, if Dover would only bring back into print MacMillan's "The Theory of the Potential" and maybe try to reprint Sternberg & Smith's U. of Toronto Press published (and out of print) "The Theory of the Potential and Spherical Harmonics", they would have themselves a trilogy to corner the science book market for the classical treatment of potential theory.
Kellogg stands fairly well on its own, but the other two books just mentioned fill-in Kellogg's gaps.
12 of 13 people found the following review helpful.
Beautiful mathematics
By David J Morley
A beautiful presentation which I much enjoyed in grad school. Now I need to return to the subject, but I can't find it in my lib. So I'm ordering another copy and looking forward to reading it again!
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