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Download e-book for iPad: Contact Geometry and Nonlinear Differential Equations by Alexei Kushner,Valentin Lychagin,Vladimir Rubtsov

By Alexei Kushner,Valentin Lychagin,Vladimir Rubtsov

tools from touch and symplectic geometry can be utilized to unravel hugely non-trivial nonlinear partial and traditional differential equations with no resorting to approximate numerical tools or algebraic computing software program. This publication explains how it is performed. It combines the readability and accessibility of a sophisticated textbook with the completeness of an encyclopedia. the elemental rules that Lie and Cartan built on the finish of the 19th century to remodel fixing a differential equation right into a challenge in geometry or algebra are right here transformed in a unique and sleek means. Differential equations are regarded as part of touch and symplectic geometry, in order that all of the equipment of Hodge-deRham calculus could be utilized. during this approach a large classification of equations could be tackled, together with quasi-linear equations and Monge-Ampere equations (which play a major function in glossy theoretical physics and meteorology).

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Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications) by Alexei Kushner,Valentin Lychagin,Vladimir Rubtsov

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