Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Symmetries and integrals -- Distributions -- Ordinary differential equations -- Model differential equations and the lie superposition principle -- Symplectic algebra -- Linear algebra of symplectic vector spaces -- Exterior algebra on symplectic vector spaces -- A symplectic classification of exterior 2-forms in dimension 4 -- Symplectic classification of exterior 2-forms -- Classification of exterior 3-forms on a six-dimensional symplectic space -- Monge-Ampère equations -- Symplectic manifolds -- Contact manifolds -- Monge-Ampère equations -- Symmetries and contact transformations of Monge-Ampère equations -- Conservation laws -- Monge-Ampère equations on two-dimensional manifolds and geometric structures -- Systems of first-order partial differential equations on two-dimensional manifolds -- Applications -- Non-linear acoustics -- Non-linear thermal conductivity -- Meteorology applications -- Classification of Monge-Ampère equations -- Classification of symplectic MAOs on two-dimensional manifolds -- Classification of symplectic MAEs on two-dimensional manifolds -- Contact classification of MAEs on two-dimensional manifolds -- Symplectic classification of MAEs on three-dimensional manifolds.

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).