<電子ブック>
Potential Theory / by Lester Helms
(Universitext. ISSN:21916675)
版 | 1st ed. 2009. |
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出版者 | (London : Springer London : Imprint: Springer) |
出版年 | 2009 |
本文言語 | 英語 |
大きさ | XI, 441 p. 2 illus : online resource |
著者標目 | *Helms, Lester author SpringerLink (Online service) |
件 名 | LCSH:Potential theory (Mathematics) LCSH:Mathematical physics LCSH:Engineering LCSH:Differential equations LCSH:Mathematics FREE:Potential Theory FREE:Mathematical Methods in Physics FREE:Technology and Engineering FREE:Differential Equations FREE:Applications of Mathematics |
一般注記 | Preliminaries -- Laplace's Equation -- The Dirichlet Problem -- Green Functions -- Negligible Sets -- Dirichlet Problem for Unbounded Regions -- Energy -- Interpolation and Monotonicity -- Newtonian Potential -- Elliptic Operators -- Apriori Bounds -- Oblique Derivative Problem Aimed at graduate students and researchers in mathematics, physics, and engineering, this book presents a clear path from calculus to classical potential theory and beyond, moving the reader into a fertile area of mathematical research as quickly as possible. The author revises and updates material from his classic work, Introduction to Potential Theory (1969), to provide a modern text that introduces all the important concepts of classical potential theory. In the first half of the book, the subject matter is developed meticulously from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem of the calculus, the author develops methods for constructing solutions of Laplace’s equation on a region with prescribed values on the boundary of the region. The second half addresses more advanced material aimed at those with a background of a senior undergraduate or beginning graduate course in real analysis. For specialized regions, namely spherical chips, solutions of Laplace’s equation are constructed having prescribed normal derivatives on the flat portion of the boundary and prescribed values on the remaining portion of the boundary. By means of transformations known as diffeomorphisms, these solutions are morphed into local solutions on regions with curved boundaries. The Perron-Weiner-Brelot method is then used to construct global solutions for elliptic partial differential equations involving a mixture of prescribed values of a boundary differential operator on part of the boundary and prescribed values on the remainder of the boundary HTTP:URL=https://doi.org/10.1007/978-1-84882-319-8 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9781848823198 |
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電子リソース |
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EB00232584 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA404.7-405 DC23:515.96 |
書誌ID | 4000116296 |
ISBN | 9781848823198 |
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※2017年9月4日以降