Global and Stochastic Analysis with Applications to Mathematical Physics by Yuri E. GliklikhGlobal and Stochastic Analysis with Applications to Mathematical Physics by Yuri E. Gliklikh

Global and Stochastic Analysis with Applications to Mathematical Physics

byYuri E. Gliklikh

Paperback | January 27, 2013

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The main aim of this book is to develop the methods of Global Analysis and of Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as quite distant from each other and requiring different methods of investigation. Among those areas we mention classical mechanics on non-linear configuration spaces, some problems of statistical and quantum physics, hydrodynamics, etc. The idea, yielding the unification of these topics, is based on the use of a geometrically invariant form of Newton's second law and its analogs (stochastic, set-valued, infinite-dimensional, etc.) as a fundamental equation of motion.
Title:Global and Stochastic Analysis with Applications to Mathematical PhysicsFormat:PaperbackDimensions:436 pagesPublished:January 27, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1447126203

ISBN - 13:9781447126201


Table of Contents

Part I Global Analysis.- Manifolds and Related Objects.- Connections.- Ordinary Differential Equations.- Elements of the Theory of Set-Valued Mappings.- Analysis on Groups of Diffeomorphisms.- Part II Stochastic Analysis.- Essentials from Stochastic Analysis in Linear Spaces.- Stochastic Analysis on Manifolds.- Mean Derivatives in Linear Spaces.- Mean Derivatives on Manifolds.- Stochastic Analysis on Groups of Diffeomorphism.- Part III Applications to Mathematical Physics.- Newtonian Mechanics.- Accessible Points and Sub-Manifolds of Mechanical Systems. Controllability.- Some Problems on Lorentz Manifolds.- Mechanical Systems with Random Perturbations.- The Newton-Nelson Equation.- Hydrodynamics.

Editorial Reviews

From the reviews:"The book is about applications of global and stochastic analysis in mathematical physics. The majority of the book reflects the work and contributions of the author and his collaborators in this field. . The author, by putting various preparation materials together, has done a good job presenting the theory in a book that for the most part is quite readable. The book is a valuable contribution to the literature, and is recommended to anyone . who is interested in problems of mathematical physics." (Ming Liao, Mathematical Reviews, Issue 2012 d)