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).

Similar differential equations books

Get Geometric Mechanics on Riemannian Manifolds: Applications to PDF

Differential geometry innovations have very valuable and demanding purposes in partial differential equations and quantum mechanics. This paintings provides a in simple terms geometric therapy of difficulties in physics concerning quantum harmonic oscillators, quartic oscillators, minimum surfaces, and Schrödinger's, Einstein's and Newton's equations.

The purpose of this guide is to acquaint the reader with the present prestige of the speculation of evolutionary partial differential equations, and with a few of its functions. Evolutionary partial differential equations made their first visual appeal within the 18th century, within the undertaking to appreciate the movement of fluids and different non-stop media.

Download PDF by Ivan G. Avramidi: Heat Kernel Method and its Applications

The guts of the e-book is the improvement of ashort-time asymptotic growth for the warmth kernel. this can be defined indetail and particular examples of a few complicated calculations are given. Inaddition a few complicated equipment and extensions, together with course integrals, jumpdiffusion and others are offered.

New PDF release: Statistical Mechanics of Disordered Systems: A Mathematical

This self-contained publication is a graduate-level advent for mathematicians and for physicists attracted to the mathematical foundations of the sphere, and will be used as a textbook for a two-semester path on mathematical statistical mechanics. It assumes purely simple wisdom of classical physics and, at the arithmetic aspect, an excellent operating wisdom of graduate-level likelihood conception.

Additional resources for Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications)

Sample text