Principles of applied mathematics

596

Book reviews

J.P. Keener,

Addison-Wesley,

Principles of Applied Mathematics,

!%48.50. ISBN

Redwood

City, 1988. XV + 560 pages, US

l-201-15674-1.

For solving problems of applied mathematics, two main principles are used: first to reduce the problem to be solved to a problem we already know how to solve and, secondly, to transform hard problems into simpler ones by ignoring small terms. These two techniques are called respectively transformation and approximation and they form the body of this book which is intended for beginning graduate students in applied mathematics. Chapter 1 deals with matrices, the second one whith function spaces. The third chapter

is devoted

variations.

The

to integral

following

equations,

chapters

the fourth to differential

respectively

treat

complex

operators variable

and the fifth to the calculus theory,

transform

and

of

spectral

theory, partial differential equations, inverse scattering transform asymptotic expansions, regular and singular perturbation theory. The book contains exercises, many examples and applications. It is extremely well written and presented. I particularly recommend it to students and also to applied mathematicians and numerical analysts. (CB) A.G. Akritas,

Elements of Computer Algebra

with Applications,

Wiley, New York, 1989. XV + 425 pages,

UK E33.75. ISBN O-471-61163-8.

This book is divided into three parts. The first one explains what computer algebra is. The second part contains the mathematical foundations and the basic algorithms, mainly the properties of integers and polynomials. The last part is devoted to applications such as error correcting codes and cryptography, computation of polynomial greatest common divisor and remainder sequences, factorization of polynomials with integer coefficients and the isolation and approximation of the real zeros of polynomials, a question whose study was the author’s own research subject. (CB) H.R. Schwan,

Numerical

Analysis,

Wiley,

Chichester,

1989. XIII + 517 pages,

UK g15.95.

ISBN

O-471-

92064-9.

This book is a very valuable reference for students in numerical analysis. engineers and scientists interested by numerical methods since it presents

It will also be useful to the basic methods and

algorithms of numerical analysis. The methods are introduced by establishing the necessary theoretical background. They are described in a form which can be easily translated into a computer program. Numerical results and examples allow to compare the various methods and to study their performances. Most of the major chapters of numerical analysis are covered and also some less usual topics. The book is well written

and clearly presented. (CB)

J. Vinuesa

(Ed.),

Orthogonal

Polynomials

and their Applications,

M. Dekker,

New York,

1989. X + 207

pages. ISBN O-8247-8161-9.

This volume contains the papers presented at an international congress held in Laredo, Spain in September 1987. There are invited papers by W. van Assche, E.A. van Doorn, J. Gilewicz, L.L. Littlejohn et al., P. Maroni, and J.L. Ullman. It also contains 11 additional communications. They deal with properties of some special families of orthogonal polynomials, orthogonality of dimension d, weighted