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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 this new edition, many exercises have been added to reconnect the subject matter to the physical sciences. This book will undoubtedly be useful to graduate students and researchers in mathematics, physics and engineering.
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 this new edition, many exercises have been added to reconnect the subject matter to the physical sciences. This book will undoubtedly be useful to graduate students and researchers in mathematics, physics and engineering.
Shows how solutions are morphed into local solutions on regions with curved boundaries
Discusses the connection between potential theory and Brownian motion
Introduces all the important concepts of classical potential theory
Equips readers for further study in elliptic partial differential equations, axiomatic potential theory and the interplay between probability theory and potential theory
Includes supplementary material: [...]
| Erscheinungsjahr: | 2014 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
xiv
485 S. 2 s/w Illustr. 485 p. 2 illus. |
| ISBN-13: | 9781447164210 |
| ISBN-10: | 1447164210 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Helms, Lester L. |
| Auflage: | 2nd edition 2014 |
| Hersteller: |
Springer London
Springer-Verlag London Ltd. |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 27 mm |
| Von/Mit: | Lester L. Helms |
| Erscheinungsdatum: | 30.04.2014 |
| Gewicht: | 0,75 kg |
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