By Alexei Kushner
Equipment from touch and symplectic geometry can be utilized to resolve hugely non-trivial nonlinear partial and traditional differential equations with no resorting to approximate numerical equipment or algebraic computing software program. This booklet explains how it truly is performed. It combines the readability and accessibility of a complicated textbook with the completeness of an encyclopedia. the fundamental rules that Lie and Cartan built on the finish of the 19th century to rework fixing a differential equation right into a challenge in geometry or algebra are right here transformed in a singular and glossy means. Differential equations are regarded as part of touch and symplectic geometry, in order that the entire equipment of Hodge-deRham calculus might be utilized. during this manner a large classification of equations might be tackled, together with quasi-linear equations and Monge-Ampere equations (which play a huge position in smooth theoretical physics and meteorology).
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