1R1. Error Analysis with Applications in Engineering. - W Szczepinski and Z Kotulski (Inst of Fund Tech Res, Polish Acad of Sci, Warsaw, Poland). Lastran Corp, Honeoye NY. 2000. 235 pp. ISBN 1-893000-02-8. \$57.00.

Reviewed by M Bonnet (Lab de Mec des Solides, Ecole Polytechnique, Route de Saclay, Palaiseau Cedex, F-91128, France).

This book comprises seven chapters, an appendix, a bibliographical section (98 references), and an index. Exercises are provided at the end of each chapter. The stated goal of the book is to address, in a simple manner, branches of error analysis finding direct applications in engineering practice.

The book can be roughly be divided into three parts. The first (Chs 1-3) presents fundamentals of error calculus. Included in this material is a survey of classical concepts from elementary probability theory (including continuous random variables) and statistics. This very classical material is presented in a rather pleasant and easy-to-read manner, but occupies a substantial fraction of the book (more than one-third). Chapters 4 and 5 are concerned with error analysis for two-dimensional functions of randomvariables. Finally, Chapters 6 and 7 are concerned with error analysis for three-dimensional functions of random variables. Chapters 4 to 7 rely strongly on linearization with respect to random parameters (either via Taylor expansion or using linear regression) and on using Gaussian distributions. The exposition is somewhat repetitious, with the same concepts presented twice (for 2D and then 3D) instead of stating once and for all the necessary concepts for $n$-dimensional situations.

The authors obviously have low-dimensional problems in mind. First of all, many of the examples are essentially geometrical in nature (eg, manipulators), and hence of either 2D or 3D. Besides, some of the methods presented are either impractical (determination of tolerance polygons by direct inspection) or infeasible (Mohr circles for the covariance matrix) in higher dimensions. On the other hand, methods better adapted to higher dimensions are not treated.

Another source of complexity is left out, namely the possibility that the $n$-dimensional functions of random parameters be defined implicitly through the solution of initial-, boundary-, or initial-boundary value problems. Similarly, no link is made to reliability analysis techniques.

Generally speaking, the computing side of error analysis is not considered. For instance, linear programing could have been invoked in connection with the determination of tolerance polygons. No mention is made either about using numerical algorithms for performing linear regressions or eigenvalue/eigenvector analyses of covariance matrices. The usefulness of computing techniques for error analysis in engineering problems of some complexity is not discussed.

This book is written in a generally clear and readable style which avoids any unnecessary complication. A substantial proportion of this relatively short book is spent on reviewing well-established concepts. The treatment of the subject lacks depth, especially regarding the absence of discussion in connection with complex modeling situations and computer-oriented treatments.

The presentation (clarity of typesetting, language,) is overall of good quality, despite some low-quality graphics and a few minor errors here and there which suggest that the publisher did not do a thorough final proofreading of the manuscript.

In conclusion, this reviewer expects Error Analysis with Applications in Engineering to be useful mostly to students and beginners in the subject area, given that the basics are presented in a relatively simple and friendly fashion. As such, it may be purchased by university libraries, although a substantial fraction of the material presented therein is already well covered in probability and statistics textbooks and monographs. On the other hand, scientists and engineers wanting to perform error analysis on complex engineering problems will probably find that the book under review falls a bit short of their objectives.