Lectures in Applied Mathematics 1996; 268 pp; softcover Volume: 31 Reprint/Revision History: reprinted 1998 ISBN10: 0821803689 ISBN13: 9780821803684 List Price: US$38 Member Price: US$30.40 Order Code: LAM/31
 This volume contains some of the lectures presented in June 1994 during the AMSSIAM Summer Seminar at the Mathematical Sciences Research Institute in Berkeley. The goal of the seminar was to introduce participants to as many interesting and active applications of dynamical systems and probabilistic methods to problems in applied mathematics as possible. As a result, this book covers a great deal of ground. Nevertheless, the pedagogical orientation of the lectures has been retained, and therefore the book will serve as an ideal introduction to these varied and interesting topics. Among the themes explored in this volume are the following:  the increasing role of dynamical systems theory in understanding partial differential equations
 the central importance of certain prototypical equations, such as the complex GinzburgLandau, nonlinear Schrödinger, and KortewegdeVries equations
 problems in fluid mechanics and the limits of physically motivated heuristic theories of fluids
 the role of probabilistic methods in studying turbulent phenomena
Readership Researchers in applied mathematics. Table of Contents Section I: Dynamical Systems and PDEs  C. E. Wayne  An introduction to KAM theory
 W. Craig  KAM theory in infinite dimensions
 N. Kopell  Global center manifolds and singularly perturbed equations: A brief (and biased) guide to (some of) the literature
 D. W. McLaughlin and J. Shatah  Melnikov analysis for PDE's
Section II: Exactly Integrable Systems  P. Deift  Integrable Hamiltonian systems
Section III: Amplitude Equations  C. D. Levermore and M. Oliver  The complex GinzburgLandau equation as a model problem
 A. Mielke and G. Schneider  Derivation and justification of the complex GinzburgLandau equation as a modulation equation
Section IV: Fluid Mechanics and Turbulence  P. Constantin  NavierStokes equations and incompressible fluid turbulence
 A. J. Chorin  Turbulence as a nearequilibrium process
 M. Avellaneda  Homogenization and renormalization: The mathematics of multiscale random media and turbulent diffusion
