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A Polynomial

and various extensions.

This well-written

book serves as a good founda-

tion to the topic of symbolic

integration.

ond volume on the integration tions will appear.

A sec-

of algebraic

func-

Highly recommendable.

Introduction

Saber

to Difference Texts

Verlag

1996, 389 pages,

Berlin,

and

in Mathematics.

: “This

the cover

equations. This book uate

analysis

Springer

ISBN

: 0-387-

modern

book

integrates

treatments

both

of difference

is intended

and beginning

for advanced

graduate

undergrad-

students,

and for

ference equations, higher order linear difference equations, and systems of difference equations. emphasis

is on the dynamics

bility of the solutions The

book

also

transform,

of equations

contains

and the staof these types.

chapters

on

control theory, asymptotic

the solutions tion theory. ciplines

books

XIII

Softcover

have already

of difference

(economics,

behavior

equations,

Many applications

the

of linear

on lin-

choice of material.

is placed on functional

els and polynomial

algebra.

tain shift operators,

defined by using polynomial

modular

form the building

arithmetic,

an arbitrary

linear operator.

Linear

gebraic

by it over the ring of polynomials. stability

sign inversion

criteria

algorithms

are investigated. for structured

it is shown that the Euclidean useful tool.

Fuhrmann

states:

tion that it no longer is possible

to separate

linear

of

approximation

theory.

seven chapters

of the book for a one-year

on linear algebra. direct

systems

papers and books.

This book is an interesting list of books

on difference

The author

addition

to the (short)

equations.

thor is one of the Editors-In-Chief

The

au-

of the Journal and as

However, the book is not always easy to read. The main problem is that it is full of misprints While reading

it I immediately

spotted at least 50 errors, from small typing errors and references to the wrong equations , to examples and exercises that are wrongly solved.

level except

the reader

to other

and additional

perhaps

norm approximation. M. Van Bare1

norm

uses the first course

At the end of each chapter,

book is self-contained

of Difference Equations and Applications, such a specialist in the field.

and other errors.

gives references

is explained

on Hankel

ends with a “Notes and Remarks”

to

in a

natural way the study of linear algebra from the study of linear systems”. Hence, the basic theory

exercises

is followed by a list of references

is a very

“It is my convic-

is devoted

are included.

AlTo de-

matrices

algorithm

of finite-dimensional

biology, . . .) are discussed.

of

tions are studied looking at the module structure

and topics not covered in the book.

Each chapter

blocks

transforma-

and a whole chapter

and oscilla-

mod-

It is shown that cer-

Z-

from different dis-

for some of them solutions

For the

and quadratic

Each section of the book is followed by a wealth of

P. Levrie

+ 360 pages,

been written

exercices, relevant

Algebra

DM 58

transformations

forms the emphasis

induced

scientists and engineers in general. It provides an introduction to the theory of first order dif-

The

O-387-94643-8,

and makes a different

Equations

DM 68

94582-2, Hardcover

classical

to Linear

Springer Verlag Berlin, 1996, ISBN: Many

N. Elaydi

Undergraduate

$rom

Approach

A. Fuhrmann

ear algebra. Here, Fuhrmann takes a different approach to the classical topics of linear algebra

P. Kravanja An

Paul

the

approaches Each chapter

section

which

comments.

The

and on the undergraduate the last chapter

on Hankel