Book Reviews 181

James A. Murdock, Perturbations n Theory and Methods. Wiley, Chiches|er, 1991, 509 pp., UK£43.65, ~SBN 0-471-61294-4.

It is the premise of this book that even at a beginning level, perturbation theory should be presented not as an isolated collection of cookbook techniques but as a part of the mainstream of mathematics. This means that theorems covered in other mathematics courses will be encoun- tered. This book makes such theorems available by a clear statement in an appendix. Throughout the book an effort has boon made to say the important things that no one ever seems to say, the simple insights tbat finally dawn after months, or even years, of working with a method. Contents: Chapter 1: Root Finding Chapter 2: Regular Perturbations Chapter 3: Direct Error Estimation Chapter 4: Periodic Solutions and Lindstedt Series Chapter 5: Multiple Scales Chapter 6: Averaging Chapter 7: Initial Layers Chapter 8: Boundary Layers Chapter 9: Methods of the WKB Type Appendices Symbol Index Index.

This book is in many ways complementary to Nayfeh's books, and certainly does not replace them. Preliminary drafts have been used in courses. The book may well become the foundation of a senior-graduate student course in perturbations.

(WFA)

C.K. Chui (ed.), Approximation Theory and Functional Analysis. Academic Press, Boston. 1990. 247 pp., US$49.95, ISBN 0-12-174583-X.

This volume was con,piled in honor of G.G. Lorentz on the occasion of his eightieth birthday. It consists of 20 invited papers, mainly surveys in approximation theory and functional analysis, the two fields to which he devoted much of his professional life. The book includes an autobiography of Lorentz, his publications and doctoral students.

(WFA)

L. Tierney, LISP-SIA I fan Object-oriented imvironment for Statistical Computing and Dynamic Graphics). Wiley, Chichester, 1990. 397 pp., UK£32.15, ISBN 0-471-50916-7.

LISP-STAT is a statistical envir:mment based on the LISP language. It includes support for vectorized arithmetic operations, a comprehensive set of basic statistical operations, an object- oriented programming system, and support for dynamic graphics.