Foundations of Potential Theory by Oliver Dimon Kellogg (PDF)

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 ok 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 Greens 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 Pirichlet problem. Exercises are introduced in the conviction that no mastery of a mathematical subject is possible without working with it. They are designed primarily to illustrate or extend the theory, although the desirability of requiring an occasional concrete numerical result has not been lost sight of.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐In graduate physics I used Jackson, Griffiths and Eyges as references and each of them bring something valuable to the table in terms of their approach, examples and derivations. This book was refreshing in that it takes the time to expand on the fundamental idea of mathematical fields and the potentials that lead to them. There is great coverage of Newtonian potentials, Green’s functions, method of images and other classic concepts that figure into the inverse square fields common in physics. This is a great reference to add to your collection if you’re interested in the subject.

⭐Classic book on PT, other books have a chapter maybe.it’s allot to adsorb.

⭐If you’re taking Jackson in grad school, you’ll need to consult this in the library or own your own copy.If you want to pass Jackson then think “where are the charges”, “what’s the field look like at infinity” and back your way into the near field.

⭐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.

⭐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!

⭐È certamente un classico nel suo genere. Purtroppo la copia ricevuta è a MIO AVVISO di pessima qualità: stampa su carta economica, che rende difficile la lettera delle formule matematiche, taglio dei fogli non bene squadrato . Quindi in linea con il basso costo del libro (edizione Isha books).I bought this book for its fame, thinking there certainly would be something in it for me, and was not disappointed.

⭐Good but old fashioned book

⭐なにせ古典の名著なので単位がSI以前のフィートポンド法なので、練習問題の単位変換が煩わしい。問題を丁寧にこなせば完璧でしょう

⭐

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