Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics (Hardcover, 1996 ed.)

The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago. The foundation of our topic is presented in the contemporary mathematical literature by a lot of publications devoted to certain parts of the above-mentioned themes and connected with the scope of material of this book. There exist some monographs on Stochastic Differential Equations on Manifolds (e. g. [9,36,38,87]) based on the Stratonovich approach. In [7] there is a detailed description of It6 equations on manifolds in Belopolskaya-Dalecky form. Nelson's book [94] deals with Stochastic Mechanics and mean derivatives on Riemannian Manifolds. The books and survey papers on the Lagrange approach to Hydrodynamics [2,31,73,88], etc. , give good presentations of the use of infinite-dimensional ordinary differential geometry in ideal hydrodynamics. We should also refer here to [89,102], to the previous books by the author [53,64], and to many others.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 374
Release date:	2001
First published:	1996
Authors:	Yuri E. Gliklikh
Dimensions:	234 x 156 x 12mm (L x W x T)
Format:	Hardcover
Pages:	192
Edition:	1996 ed.
ISBN-13:	978-0-7923-4154-3
Categories:	Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers
LSN:	0-7923-4154-6
Barcode:	9780792341543

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