Download stochastic tools in mathematics and science 1 surveys and tutorials in the applied mathematical sciences in pdf or read stochastic tools in mathematics and science 1 surveys and tutorials in the applied mathematical sciences in pdf online books in PDF, EPUB and Mobi Format. Click Download or Read Online button to get stochastic tools in mathematics and science 1 surveys and tutorials in the applied mathematical sciences in pdf book now. This site is like a library, Use search box in the widget to get ebook that you want.



Stochastic Tools In Mathematics And Science

Author: Alexandre J Chorin
Publisher: Springer Science & Business Media
ISBN: 1441910026
Size: 69.72 MB
Format: PDF, ePub, Mobi
View: 4002
Download and Read
This introduction to probability-based modeling covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. Topics covered include conditional expectations, stochastic processes, Langevin equations, and Markov chain Monte Carlo algorithms. The applications include data assimilation, prediction from partial data, spectral analysis and turbulence. A special feature is the systematic analysis of memory effects.

Applied Delay Differential Equations

Author: Thomas Erneux
Publisher: Springer Science & Business Media
ISBN: 0387743723
Size: 17.49 MB
Format: PDF, Mobi
View: 2878
Download and Read
Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations. Written to a multi-disciplinary audience, it sets each area of science in his historical context and then guides the reader towards questions of current interest.

An Introduction To Computational Stochastic Pdes

Author: Gabriel J. Lord
Publisher: Cambridge University Press
ISBN: 1139915770
Size: 37.10 MB
Format: PDF, ePub, Mobi
View: 341
Download and Read
This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science.

An Introduction To Fronts In Random Media

Author: Jack Xin
Publisher: Springer Science & Business Media
ISBN: 0387876839
Size: 46.39 MB
Format: PDF, ePub
View: 1247
Download and Read
This book aims to give a user friendly tutorial of an interdisciplinary research topic (fronts or interfaces in random media) to senior undergraduates and beginning grad uate students with basic knowledge of partial differential equations (PDE) and prob ability. The approach taken is semiformal, using elementary methods to introduce ideas and motivate results as much as possible, then outlining how to pursue rigor ous theorems, with details to be found in the references section. Since the topic concerns both differential equations and probability, and proba bility is traditionally a quite technical subject with a heavy measure theoretic com ponent, the book strives to develop a simplistic approach so that students can grasp the essentials of fronts and random media and their applications in a self contained tutorial. The book introduces three fundamental PDEs (the Burgers equation, Hamilton– Jacobi equations, and reaction–diffusion equations), analysis of their formulas and front solutions, and related stochastic processes. It builds up tools gradually, so that students are brought to the frontiers of research at a steady pace. A moderate number of exercises are provided to consolidate the concepts and ideas. The main methods are representation formulas of solutions, Laplace meth ods, homogenization, ergodic theory, central limit theorems, large deviation princi ples, variational principles, maximum principles, and Harnack inequalities, among others. These methods are normally covered in separate books on either differential equations or probability. It is my hope that this tutorial will help to illustrate how to combine these tools in solving concrete problems.

Vorticity And Turbulence

Author: Alexandre J. Chorin
Publisher: Springer Science & Business Media
ISBN: 1441987282
Size: 15.59 MB
Format: PDF, ePub, Docs
View: 476
Download and Read
This book provides an introduction to the theory of turbulence in fluids based on the representation of the flow by means of its vorticity field. It has long been understood that, at least in the case of incompressible flow, the vorticity representation is natural and physically transparent, yet the development of a theory of turbulence in this representation has been slow. The pioneering work of Onsager and of Joyce and Montgomery on the statistical mechanics of two-dimensional vortex systems has only recently been put on a firm mathematical footing, and the three-dimensional theory remains in parts speculative and even controversial. The first three chapters of the book contain a reasonably standard intro duction to homogeneous turbulence (the simplest case); a quick review of fluid mechanics is followed by a summary of the appropriate Fourier theory (more detailed than is customary in fluid mechanics) and by a summary of Kolmogorov's theory of the inertial range, slanted so as to dovetail with later vortex-based arguments. The possibility that the inertial spectrum is an equilibrium spectrum is raised.

A Natural Introduction To Probability Theory

Author: R. Meester
Publisher: Springer Science & Business Media
ISBN: 9783764387242
Size: 74.51 MB
Format: PDF, ePub
View: 5865
Download and Read
Compactly written, but nevertheless very readable, appealing to intuition, this introduction to probability theory is an excellent textbook for a one-semester course for undergraduates in any direction that uses probabilistic ideas. Technical machinery is only introduced when necessary. The route is rigorous but does not use measure theory. The text is illustrated with many original and surprising examples and problems taken from classical applications like gambling, geometry or graph theory, as well as from applications in biology, medicine, social sciences, sports, and coding theory. Only first-year calculus is required.