Books in the Applied Mathematical Sciences series

This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes the fundamental ideas of the past two decades of research, carefully balancing theory and application.

This book covers adaptive mesh generation and moving mesh methods for solving time-dependent PDEs. It gives a general description of the components of moving mesh methods as well as examples of their application for a number of nontrivial physical problems.

This mathematically rigorous survey of the special theory of relativity also details the physical significance of that mathematics. In addition to kinematics, particle dynamics and electromagnetic fields it treats subjects usually bypassed at elementary level.

Focusing on large-amplitude patterns far from equilibrium in biologically relevant models, this book summarizes and expands on fifteen years of results in the mathematical analysis of patterns which are encountered in biological systems.

This book deals with optimality conditions, algorithms, and discretization tech niques for nonlinear programming, semi-infinite optimization, and optimal con trol problems.

Brownian dynamics play a key role in molecular and cellular biophysics. This book is aimed at applied mathematicians, physicists, theoretical chemists and physiologists interested in the modeling, analysis and simulation of micro devices of microbiology.

This book summarizes effective and general approaches and frameworks in the investigation of bifurcation phenomena for functional differential equations (FDEs). It provides all the tools from bifurcation theory and contains examples and applications.

This book introduces mathematical techniques needed to analyse PDEs coming from incompressible fluid mechanics, including Stokes and Navier-Stokes equations and more specific models, and offering methods applicable to a range of domains in nonlinear analysis.

This book is devoted to an account of theories of heat conduction where the temperature may travel as a wave with a finite speed. It surveys many of the theories which have been proposed as candidates to describe thermal motion as a wave.

Transient Chaos provides an overview of the field, based on a summation of nearly three decades of intensive research. Written by experts in the field, this volume shows why transient chaos is important to the nonlinear-science community, as well as other scientific disciplines.

This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. The book also develops basic differential geometrical concepts centred about curvature.

This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD).

Dynamical Systems and Chaos provides an overview of the field that bridges the gap between abstract and applied areas of study. Exercises included at the end of each chapter illustrate the concepts discussed, and are appropriate for undergraduate and graduate courses, alike.

Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more.

Ludwig Prandtl has been called the father of modern fluid mechanics, and this updated and extended edition of his classic text on the field is based on the 12th German edition with additional material included.

The second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, and their substantial applications.

The author presents the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented.

I was guided by the desire to prove, as simply as possible, that, like systems of n linear algebraic equations in n unknowns, the solvability of basic boundary value (and initial-boundary value) problems for partial differential equations is a consequence of the uniqueness theorems in a "sufficiently large" function space.

This book examines the basic mathematical properties of solutions to boundary integral equations and details the variational methods for the boundary integral equations arising in elasticity, fluid mechanics and acoustic scattering theory.

Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns.

This book is developed for the study of vectorial problems in the calculus of variations. It is a new edition of the earlier book published in 1989. Almost half of the book consists of new material and there are added examples.