03534nam a22005655i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001900153050001600172072001600188072001700204072002300221082001400244100003200258245010800290250001200398264004600410300004100456336002600497337002600523338003600549347002400585490006800609505015300677520150100830650001702331650002502348650002902373650001902402650002302421650002502444650002302469650002102492650001702513650004902530650005902579650003302638650003302671650003202704700002602736710003402762773002002796776003602816830006802852856004802920978-1-4419-1002-8DE-He21320180115171456.0cr nn 008mamaa100715s2009 xxu| s |||| 0|eng d a97814419100287 a10.1007/978-1-4419-1002-82doi 4aQA273.A1-274.9 4aQA274-274.9 7aPBT2bicssc 7aPBWL2bicssc 7aMAT0290002bisacsh04a519.22231 aChorin, Alexandre.eauthor.10aStochastic Tools in Mathematics and Scienceh[electronic resource] /cby Alexandre Chorin, Ole H. Hald. asecond. 1aNew York, NY :bSpringer New York,c2009. aX, 162 p. 7 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aSurveys and Tutorials in the Applied Mathematical Sciences ;v10 aPreliminaries -- Probability -- Brownian Motion -- Stationary Stochastic Processes -- Statistical Mechanics -- Time-Dependent Statistical Mechanics. aStochastic 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). 0aMathematics. 0aApplied mathematics. 0aEngineering mathematics. 0aProbabilities. 0aContinuum physics. 0aStatistical physics. 0aDynamical systems. 0aFluid mechanics.14aMathematics.24aProbability Theory and Stochastic Processes.24aStatistical Physics, Dynamical Systems and Complexity.24aClassical Continuum Physics.24aApplications of Mathematics.24aEngineering Fluid Dynamics.1 aHald, Ole H.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781441910011 0aSurveys and Tutorials in the Applied Mathematical Sciences ;v140uhttp://dx.doi.org/10.1007/978-1-4419-1002-8