424
Book reviews
R.K. Livesley, Mathematical Methods for Engineers. Ellis Horwood, Chichester, 215.95, ISBN o-7458-0714-3.
1989. 462 pp.,
This book is intended for students in engineering. It is divided into three parts: vectors and matrices, functions of a single variable, functions of several independent variables. The methods are illustrated by examples from engineering. (CB) L. Jacobsen (ed.), Analytic Theory of Continued Fractions III, Lecture Notes in Mathematics 1406. Springer, Berlin, 1989. 142 pp., DM 25, ISBN 3-540-51830-4. This volume contains the papers presented during a workshop held in July 1988. They deal with the analytic theory of continued fractions, are written by well-known experts of the question and are intended for researchers in the field who should have this book. (CB) S. Kesavan, Topics in Functional Analysis and Applications. Wiley, New York, 1989, 267 pp., E20.15, ISBN O-470-21050-8 (Wiley, NY); 81-224-0062-o (Wiley Eastern). The goal of this book is to provide a course on functional analytic methods used in the study of partial differential equations. The first chapter covers the main aspects of the theory of distributions and the Fourier transform. The notion of distribution solutions to partial differential equations is introduced. The second chapter studies the important properties of Sobolev spaces. These spaces form a natural functional analytic framework for the study of weak solutions of elliptic boundary value problems which is the topic discussed in chapter three. Here is studied the existence, uniqueness and regularity of weak solutions of linear elliptic boundary value problems. The general theory is illustrated by several examples from physics and engineering. The maximum principle and eigenvalue problems are also considered. The fourth chapter is devoted to the study of evolution equations using the theory of semigroups of linear operators on a Banach space. After a brief introduction to the abstract theory, illustrations via some standard partial differential equations are provided. The last chapter provides an introduction to the study of semi-linear elliptic boundary value problems from the point of fixed-point theorems, aperoximation methods and variational principles. Comments at the end of each chapter provide additional information or results not given in the text and also give important references. Each chapter is also provided with a selection of exercises. (WFA) B.A. Plamenevskii, Algebras of Pseudodifferential Operators, Volume 43, Mathematics and its Applications (Soviet Series). Khrwer, Dordrecht, 1989. 291 pp., Dfl. 210, US $99, ti9, ISBN 0-7923-0231-l. This is a translation of the original 1986 Nauka edition. Growing out of integral operators this subject has been created in the last thirty years. A number of texts treat one-dimensional singular