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Contact geometry and non-linear differential equations /
Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibil...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
2007.
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| Colección: | Encyclopedia of mathematics and its applications ;
volume 101. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology). |
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| Descripción Física: | 1 online resource (xxi, 496 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 487-492) and index. |
| ISBN: | 9781461941484 1461941482 9780511735141 0511735146 1139883089 9781139883085 0511889755 9780511889752 1107383935 9781107383937 1107387442 9781107387447 1107390362 9781107390362 1107398770 9781107398771 |