Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics

By: Yuri E. Gliklikh

Write A Review

Hardcover | 31 August 1996

At a Glance

Hardcover
212 Pages

Dimensions(cm)
25.4 x 17.15 x 1.91

Hardcover

$169.00

or 4 interest-free payments of $42.25 with

Ships in 5 to 7 business days

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.

Industry Reviews

` ... the author has successfully arranged them [the topics] into a smooth, coherent rexposition. It is highly recommended for those readers with good background knowledge in differential geometry, stochastic analysis, and mathematical physics.'
Mathematical Reviews, 98k

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Science Physics Mathematical Physics Mathematics Geometry Differential & Riemannian Geometry Applied Mathematics Calculus & Mathematical Analysis Science in General Maths for Scientists Probability & Statistics

Acknowledgements
Introduction
Elements of Coordinate-Free Differential Geometry	p. 1
Introduction to Stochastic Analysis in R[superscript n]	p. 45
Stochastic Differential Equations on Manifolds	p. 75
Langevin's Equation in Geometric Form	p. 99
Nelson's Stochastic Mechanics	p. 107
The Lagrangian Approach to Hydrodynamics	p. 137
Solution of the Newton - Nelson equation with random initial data	p. 166
References	p. 175
Index	p. 183
Table of Contents provided by Blackwell. All Rights Reserved.

Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Differential & Riemannian Geometry

Lectures on Differential Geometry I

Differentiable Manifolds

Geometric Methods in Physical Systems

From Differentiable Structures to Applications, the Wisla 22 Winter School and Workshop

Complex Analysis in One Variable and Riemann Surfaces

Graduate Texts in Mathematics

Geometry of Integrable Systems

An Introduction

Liouville's Theory in Linear and Nonlinear Partial Differential Equations

Springer Asia Pacific Mathematics

Consensus and Synchronization

From the Euclidean Space and the Circle to Lie Groups

An Introduction to Sympletic Geometry

Graduate Studies in Mathematics

Concise Complex Analysis

Collected Papers of Y. Matsushima

SERIES IN PURE MATHEMATICS

Harmonic Maps

Topics in Integral Geometry

Series in Pure Mathematics

Two Reports on Harmonic Maps

Introductory Differential Geometry for Physicists

The Arnoldfest : Proceedings of a Conference in Honour of V. I. Arnold for His 60th Birthday

Fields Institute Communications

Least Action Principle of Crystal Formation of Dense Packing Type and the Proof of Kepler's Conjecture

Nankai Tracts in Mathematics

Lectures on Chern-Weil Theory and Witten Deformations

Nankai Traits in Mathematics

Backlund and Darboux Transformations : The Geometry of Solitons: AARMS-CRM Workshop, June 4-9, 1999, Halifax, N. S., Canada

Crm Proceedings and Lecture Notes

An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

Volume 120

Interpolation and Sampling in Spaces of Analytic Functions

University Lecture Series

Web Theory and Related Topics

Chirurgie des Grassmanniennes

Crm Monograph Series

Trends in Complex Analysis, Differential Geometry and Mathematical Physics

Surfaces with Constant Mean Curvature

Translations of Mathematical Monographs

Lectures on Elliptic and Parabolic Equations in Holder Spaces

Graduate Studies in Mathematics

This product is categorised by