B O O K - - R E VII E W S

M u l t i g r i d M e t h o d s I I Proceedings of the 2nd European Conference on Multigrid Methods, held at Cologne, October 1-4, 1985 Editors: W. Hackbusch and U. Trottenberg Springer-Verlag, Lecture Notes in Mathematics, Vol 1228, Edited by A. Dold and B. Eckman, ISBN: 3 540 17198 3

The proceedings of the 2nd European Conference on Multi- grid Methods reflect the great progress achieved in the last four years in the breakthrough of the multigrid idea to field application problems.

Most of the papers published in this volume deal with problems arising from fluid and aerodynamics. They are of interest for a large number of scientists in both the aca- demic and industrial research communities.

New fields of applications as well as classical numerical problems are treated here. Among these, are local mesh refinements, error estimates, continuation techniques for nonlinear steady state problems, multigrid and conjugate gradients, indefinite problems and the treatment of singu- larities.

Parallel computing is another topic dealt with in this volume. There are two papers treating parallel multigrid algorithms.

In conclusion, this is a reference book in the field of Multigrid Methods.

Artur Portela Computational Mechanics Institute, Southampton, UK

A d a p t i v e M e t h o d s for P a r t i a l D i f fe ren t i a l Equations edited by J.E. Fiaherty, P.J. Paslow, M.S. Shephard and J.D Vasilakis Siam-Philadelphia, 1989, ISBN: 0-89871-242-4

This book includes edited versions of papers presented at the second workshop on adaptive computational meth- ods for partial differential equations which was held in Troy, New York in 1988.

The book is concerned with the great progress achieved over the last few years on developing reliable, robust and efficient software applying adaptive strate- gies using mesh refinement (h), mesh redistribution (r) or basis enrichment (p). Some papers also include the advantages of combining h and p refinements.

Some papers deal with the a priori or a posteriori computation of errors in order to perform a computa- tionally better grid, chosen as a trade-off between fine- ness and solution accuracy and coarseness for CPV time efficiency.

Overall, the papers are related with a broad spec- trum of ideas such as reliability of computations, method of lines, time dependent problems, diffusion, fluid flow and dynamics and three-dimensional applications.

In short, the book presents a realistic and represcn- tative picture of today's state of the art ill adaptive methods to solve many challenging research and engi- neering problems.

J.S.P. Cabral Computational Mechanics Institute Southampton, U.K. (On leave from Water Resources and Environmental Engineering Group Federal University of Pernambuco Recife, Brazil}

Calcu lus a n d A n a l y t i c G e o m e t r y 7th Edition by G.B. Thomas and R.L. Finney Addison-Wesley Publishers Limited, 1988, 1136 pp, £20.95, ISBN: 0-201-17069-8

This book provides the necessary tools for a sound un- derstanding of calculus and analytic geometry. It is one of the most comprehensive revisions of the calcu- lus field available. The strength of the book lies in its orientation towards application and its concentration on worked examples, and the number and variety of the exercises. The beauty of the text lies in its nu- merous highlighted figures which enable the reader to visualise curves, surfaces and solids in both two and three-dimensional space. Each chapter begins with an overview that connects the forthcoming material with other topics in the book and describes its importance in theory and application. Quick reference charts are also included displaying groups of related formulas and describing problem-solving strategies.

In conclusion, I would thoroughly recommend this book for 'A' level mathematics and first year univer- sity students in engineering. The book can be used as a quick, up to date reference on calculus and analytic geometry.

Contents. 1. The rate of change of a function; 2. Derivatives; 3. Applications of derivatives; 4. Integra- tion; 5. Applications of definite integrals; 6. Transcen- dental functions; 7. Methods of integration; 8. Conic sections and other plane curves; 9. Hyperbolic func- tions; 10. Polar coordinates; 11. Infinite sequences and infinite series; 12. Power series; 13. Vectors; 14. Vector functions and motion; 15. Surfaces, coordinate systems and drawing; 16. Functions of two or more variables and their derivatives; 17. Applications of par- tial derivatives; 18. Multiple integrals; 19. Vector fields and integration; 20. Differential equations.

R. Bains. Computational Mechanics Institute Southampton, U.K.

Adv. Eng. Software, Vol. 13, No. 1 53