Potential Theory. 2nd ed. 2014

種類:

電子ブック

責任表示:

by Lester L. Helms

出版情報:

London : Springer London : Imprint: Springer, 2014

著者名:

• Helms, Lester L.
• SpringerLink (Online service)

シリーズ名:

Universitext ;

ISBN:

9781447164227 [1447164229]    

注記:

Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In

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