Stochastic Tools in Mathematics and Science
Chorin, Alexandre.
creator
author.
Hald, Ole H.
author.
SpringerLink (Online service)
text
xxu
2009
second.
monographic
eng
access
X, 162 p. 7 illus. online resource.
Stochastic Tools in Mathematics and Science is an introductory book on probability-based modeling. It covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, renormalization and dimensional reduction, and basic equilibrium and non-equilibrium statistical mechanics. The applications include data assimilation, prediction from partial data, spectral analysis, and turbulence. A noteworthy feature of the book is the systematic analysis of memory effects. In this second edition, the new topics include Feynman diagrams and a new discussion of the renormalization group. The book is based on lecture notes from a class that has attracted graduate and advanced undergraduate students from mathematics and from many other science departments at the University of California, Berkeley. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications. "Chorin and Hald provide excellent explanations with considerable insight and deep mathematical understanding, especially toward the end of the book in the context of simplified versions of the famous statistical mechanics models of Ising and of Mori and Zwanzig." (SIAM Review).
Preliminaries -- Probability -- Brownian Motion -- Stationary Stochastic Processes -- Statistical Mechanics -- Time-Dependent Statistical Mechanics.
by Alexandre Chorin, Ole H. Hald.
Mathematics
Applied mathematics
Engineering mathematics
Probabilities
Continuum physics
Statistical physics
Dynamical systems
Fluid mechanics
Mathematics
Probability Theory and Stochastic Processes
Statistical Physics, Dynamical Systems and Complexity
Classical Continuum Physics
Applications of Mathematics
Engineering Fluid Dynamics
QA273.A1-274.9
QA274-274.9
519.2
Springer eBooks
Surveys and Tutorials in the Applied Mathematical Sciences ; 1
9781441910028
http://dx.doi.org/10.1007/978-1-4419-1002-8
http://dx.doi.org/10.1007/978-1-4419-1002-8
100715
20180115171456.0
978-1-4419-1002-8