This marks the 100th volume to appear in the Applied Mathematical Sci- ences series. Partial Differential Equations, by Fritz John, the first volume of the series, appeared in 1971. One year prior to its appearance, the then mathematics editor of Springer-Verlag, Klaus Peters, organized a meeting to look into the possibility of starting a series slanted toward applications. The meeting took place in New Rochelle, at the home of Fritz and Char- lotte John. K.O. Friedrichs, Peter Lax, Monroe Donsker, Joe Keller, and others from the Courant Institute (previously, the Institute for Mathemat- ical...

This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer- Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal...

This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms.

"Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."--MATHEMATICAL REVIEWS

The aim of this book is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple, yet rich, class of examples, that is, those described by delay differential equations. It is a textbook giving detailed proofs and providing many exercises, which is intended both for self-study and for courses at a graduate level. The book would also be suitable as a reference for basic results. As the subtitle indicates, the book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the...

Hysteresis is an exciting and mathematically challenging phenomenon that oc- curs in rather different situations: jt, can be a byproduct offundamental physical mechanisms (such as phase transitions) or the consequence of a degradation or imperfection (like the play in a mechanical system), or it is built deliberately into a system in order to monitor its behaviour, as in the case of the heat control via thermostats. The delicate interplay between memory effects and the occurrence of hys- teresis loops has the effect that hysteresis is a genuinely nonlinear phenomenon which is usually...

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. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential...

In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.

This book presents a development of invariant manifold theory for a spe- cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec- ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds. The central technique for proving these results is Hadamard's graph transform method generalized to an infinite-dimensional setting. However, our setting is somewhat...

The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

This book is devoted to the study of the acoustic wave equation and of the Maxwell system, the two most common wave equations encountered in physics or in engineering. The main goal is to present a detailed analysis of their mathematical and physical properties. Wave equations are time dependent. However, use of the Fourier trans- form reduces their study to that of harmonic systems: the harmonic Helmholtz equation, in the case of the acoustic equation, or the har- monic Maxwell system. This book concentrates on the study of these harmonic problems, which are a first step toward the study of...