Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics

Gliklikh Yuri E.

ISBN 10: 0792341546 / ISBN 13: 9780792341543

Published by Springer, 1996

About this Item

Print on Demand pp. 212 52:B&W 6.14 x 9.21in or 234 x 156mm (Royal 8vo) Case Laminate on White w/Gloss Lam.

Seller Inventory # 8379578

Bibliographic Details

• Title: Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics
• Publisher: Springer
• Publication Date: 1996
• Language: English
• ISBN 10: 0792341546
• ISBN 13: 9780792341543
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

Product Description

Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics Includes applications such as the Langevin equation of statistical mechanics. This book also covers Nelson's stochastic mechanics (a version of quantum mechanics), and the hydrodynamics of viscous incompressible fluid treated with the modern Lagrange formalism. Full description