Contact geometry and non-linear differential equations / Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov
Tipo de material:
TextoSeries Encyclopedia of mathematics and its applications ; 101Detalles de publicación: Cambridge, UK ; New York : Cambridge University Press, 2007 Descripción: xxi, 496 p. : ilISBN: 9780521824767Otro título: Contact geometry and nonlinear differential equationsTema(s): Ecuaciones diferenciales no lineales | GeometríaResumen: 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)
| Tipo de ítem | Biblioteca de origen | Signatura | Estado | Fecha de vencimiento | Código de barras | Reserva de ítems |
|---|---|---|---|---|---|---|
| Monografías | 02. BIBLIOTECA CAMPUS PUERTO REAL | 517.9/KUS/con (Navegar estantería(Abre debajo)) | Prestado | 31/01/2025 | 3744947978 | |
| Monografías | 02. BIBLIOTECA CAMPUS PUERTO REAL | 517.9/KUS/con (Navegar estantería(Abre debajo)) | Prestado | 31/01/2025 | 3744891485 |
Incluye referencias bibliográficas (p. 487-492) e Índice
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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