Bücher der Reihe Applied Mathematical Sciences

We concentrate our efforts on this method, not because we underrate those which appear more powerful in some circumstances, but because it is important enough, along with its modern developments, to justify the writing of an up-to-date monograph.

The book deals with a powerful and convenient approach to a great variety of types of problems of the recursive monte-carlo or stochastic approximation type. The approach, relating algorithm behavior to qualitative properties of deterministic or stochastic differ ential equations, has advantages in algorithm conceptualiza tion and design.

This approach makes it possible to treat a seemingly broad range of equations from nonautonomous ordinary differential equa tions and partial differential equations to stochastic differ ential equations. This space serves as the phase space for the semidynamical system.

The aim of the seminars was to present geometric quantization from the point of view* of its applica tions to quantum mechanics, and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems.

The first to examine topological, group-theoretic and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified viewpoint, this book describes preliminary notions in hydrodynamics and pure mathematics with numerous examples and figures.

The idea for this book was conceived by the authors some time in 1988, and a first outline of the manuscript was drawn up during a summer school on mathematical physics held in Ravello in September 1988, where all three of us were present as lecturers or organizers.

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.

An exposition of the derivation and use of equations of motion for two-phase flow. The work focuses on the fundamental aspects of two-phase flow, and is intended to give the reader a background for understanding the dynamics as well as a system of equations that can be used in predictions of the behavior of dispersed two-phase flows.

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

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.

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.

This illustrated book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods are used to examine experimental and computational data from numerous examples (soil, sand, kaolin, concrete, domes).

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry.

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 treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic.

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.

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.

'Exact' and 'heuristic' techniques are enhancing our ability to overcome intractable obstacles in the world of optimization. Using the linear ordering problem as an illustration, this text provides a toolkit for tackling a variety of combinatorial dilemmas.

Compactly supported smooth piecewise polynomial functions provide an efficient tool for the approximation of curves and surfaces and other smooth functions of one and several arguments.

This book covers the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves.

This monograph presents the recently introduced and already widely referred semi-discretization method for the stability analysis of delayed dynamical systems. The semi-discretization method is presented in a simple and clear way with examples.

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.

This volume is intended to provide a comprehensive treatment of recent developments in methods of perturbation for nonlinear systems of ordinary differ ential equations. The main goal is to describe perturbation techniques, discuss their ad vantages and limitations and give some examples.

The present lectures intend to provide an introduction to the spectral analysis of self-adjoint operators within the framework of Hilbert space theory. Next, simple differential operators are treated as operators in Hilbert space, and the final chapter deals with the perturbation of discrete and continuous spectra.

This book offers an analytical rather than measure-theoretical approach to the derivation of the partial differential equations of nonlinear filtering theory.

This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.