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Book review

Author(s) Elworthy, K.D. (ed.)
Everitt, W. Norrie (ed.)
Lee, E. Bruce (ed.)
Title Differential Equations, Dynamical Systems, and Control Science
Publisher Marcel Dekker
Year of publication 1993
Reviewed by Viorica-Cerasela Postolache

This major book provides the proceedings of the Conference organized in honour of Lawrence Markus on the occasion of his seventieth birthday. The book exhibits the papers in their full length, together proofs and references.

Divided into two parts this volume presents new researches in differential equations and dynamical systems as well as interesting open problems etc. The first part, Differential Equations, deals with competitive Lotka-Volterra systems, Bessel's functions and Lyapunov functions, stability criteria together necessary and sufficient conditions for stability, stochastic oscillations, asymptotic and numerical methods (e.g. for Schrodinger's equation, Navier-Stokes equations), algorithms. The second part, Dynamical Systems and Control Science, contains subtopics such that: optimal control, data analysis, vector field approximation, two-dimensional systems, ergodic systems etc. This volume can be recommended as a supplementary graduate text. Also, the book can be used with advantage by prospective mathematicians from universities and, perhaps, by mathematically inclined engineers.

Intended to attract readers interested both in theory and applications the book includes modern topics such that: numerical examples, convergence analysis of treated algorithms, robust stability, parameter dependence of solutions and emphasizes connections in physics, biology, mechanics, real and complex analysis. Examples and carefully plotted pictures, illustrate the ideas and the concepts. This research level book is very well written all concepts being clearly presented. No index, but the table of contents is enough detailed.

This material provides original research papers some of these having survey-type character. The book being very high specialized is designed mainly for the institutional market and for individuals seriously interested in the topic. Reading calls for acquaintance with elements of calculus.

Of course, the book is very well realized but the works have not unitary appearance. Someone are one row-written and another two (!) rows. This made the book very sizable (946 pp.) and very expensive (US$. 195).