Free Delivery Over $100
|
|
|||
|
||||
OverviewThis book gives a common treatment to three areas of application of Global analysis to Mathematical Physics previously considered quite distant from each other. These areas are the geometry of manifolds applied to classical mechanics, stochastic differential geometry used in quantum and statistical mechanics, and infinite-dimensional differential geometry fundamental for hydrodynamics. Full Product DetailsAuthor: Yuri E. Gliklikh , V. L. GinzburgPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 1997 ed. Volume: 122 Dimensions: Width: 15.50cm , Height: 1.40cm , Length: 23.50cm Weight: 0.524kg ISBN: 9780387948676ISBN 10: 0387948678 Pages: 216 Publication Date: 13 December 1996 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of print, replaced by POD  We will order this item for you from a manufatured on demand supplier. Table of ContentsI. Finite-Dimensional Differential Geometry and Mechanics.- 1 Some Geometric Constructions in Calculus on Manifolds.- 2 Geometric Formalism of Newtonian Mechanics.- 3 Accessible Points of Mechanical Systems.- II. Stochastic Differential Geometry and its Applications to Physics.- 4 Stochastic Differential Equations on Riemannian Manifolds.- 5 The Langevin Equation.- 6 Mean Derivatives, Nelson’s Stochastic Mechanics, and Quantization.- III. Infinite-Dimensional Differential Geometry and Hydrodynamics.- 7 Geometry of Manifolds of Diffeomorphisms.- 8 Lagrangian Formalism of Hydrodynamics of an Ideal Incompressible Fluid.- 9 Hydrodynamics of a Viscous Incompressible Fluid and Stochastic Differential Geometry of Groups of Diffeomorphisms.- Appendices.- A. Introduction to the Theory of Connections.- Connections on Principal Bundles.- Connections on the Tangent Bundle.- Covariant Derivatives.- Connection Coefficients and Christoffel Symbols.- Second-Order Differential Equations and the Spray.- The Exponential Map and Normal Charts.- B. Introduction to the Theory of Set-Valued Maps.- C. Basic Definitions of Probability Theory and the Theory of Stochastic Processes.- Stochastic Processes and Cylinder Sets.- The Conditional Expectation.- Markovian Processes.- Martingales and Semimartingales.- D. The Itô Group and the Principal Itô Bundle.- E. Sobolev Spaces.- F. Accessible Points and Closed Trajectories of Mechanical Systems (by Viktor L. Ginzburg).- Growth of the Force Field and Accessible Points.- Accessible Points in Systems with Constraints.- Closed Trajectories of Mechanical Systems.- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
||||
