The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great- est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak- ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im- portant, since they played a leading role in the development of some...

1. 1. Overview of Numerical Quadrature The numerical evaluation of integrals is one of the oldest problems in mathematics. One can trace its roots back at least to Archimedes. The task is to compute the value of the definite integral of a given function. This is the area under a curve in one dimension or a volume in several dimensions. In addition to being a problem of great practi- cal interest it has also lead to the development of mathematics of much beauty and insight. Many portions of approximation theory are directly applicable to integration and results from areas as diverse as...

This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.

LANCELOT is a software package for solving large-scale nonlinear optimization problems. This book is our attempt to provide a coherent overview of the package and its use. This includes details of how one might present examples to the package, how the algorithm tries to solve these examples and various technical issues which may be useful to implementors of the software. We hope this book will be of use to both researchers and practitioners in nonlinear programming. Although the book is primarily concerned with a specific optimization package, the issues discussed have much wider implications...

Reaction-diffusion equations are typical mathematical models in biology, chemistry and physics. These equations often depend on various parame- ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ- ent substances. The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters. Cor- respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions. This kind of phe-...

A succinct introduction to etale cohomology. Well-presented and chosen this will be a most welcome addition to the algebraic geometrist's library.

Most of the texts available on lasers deal with laser engineering and laser applications, only a few of them treating theoretical aspects of the laser at an advanced level. Introduction to Laser Physics provides an introduction to the essential physics of quantum electronics and lasers. Fundamental topics in modern optics, the applicability of various theoretical approaches, and the physical meaning of laser-related phenomena are carefully described. Experimental results and properties of practical lasers are interwoven, thereby allowing an explicit demonstration of the rate equation...

Kepler's Physical Astronomy is an account of Kepler's reformulation of astronomy as a physical science, and of his successful use of (incorrect) physics as a guide in his astronomical discoveries. It presents the only reliable account of the internal logic of Kepler's so-called first and second laws, showing how and to what extent Kepler thought he had derived them from his physical principles. It explains for the first time Kepler's attempt to use an obscure discovery of Tycho Brahe to unify and confirm all of his own physical theories. It also describes the intricate (and neglected)...

Learning from experience, making decisions on the basis of the available information, and proceeding step by step to a desired goal are fundamental behavioural qualities of human beings. Nevertheless, it was not until the early 1940's that such a statistical theory - namely Sequential Analysis - was created, which allows us to investigate this kind of behaviour in a precise manner. A. Wald's famous sequential probability ratio test (SPRT; see example (1.8- turned out to have an enormous influence on the development of this theory. On the one hand, Wald's fundamental monograph "Sequential...

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.