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Cover of Exploring Nature's Dynamics Exploring Nature's Dynamics

E. Atlee Jackson, John Wiley, 2001, 326 pp., price £ 57.50;
Level: introductory.
There are many introductory books on nonlinear dynamics and they are of varying quality; this is a good one. About the use of models, population dynamics with the bifurcation jungle, differential equations and chaos. There are many references and erudite background material. Included is a disc to run MS DOS programs for exploration.
Cover of Small Groups as Complex Systems Small Groups as Complex Systems

H. Arrow, J.E. McGrath and J.L. Berdahl, Sage Publications, Inc., 2000, 344 pp., price US$ 36.95 (pbk).
Level: introductory.
Sociologists inspired by complexity theory and dynamical systems are looking at the dynamics of small groups in human society. Formation, development and adaptation are the key words but without formulas and very few figures. It would be a good thing if mathematicians would look at this daring enterprise and would make contact with sociology.
  Symmetry and Perturbation Theory

Giuseppe Gaeta (ed.), Acta Applicandae Mathematicae vol. 70, nos. 1-3, 2002, 282 pp.
Level: medium to advanced.
Twelve tutorial papers on long time stability, normal forms, equivariant reduction, parametric resonance and molecular dynamics.
Cover of Dynamical Systems, from crystal to chaos Dynamical Systems, from crystal to chaos
Proceedings of Conference in honor of Gerard Rauzy

J.-M. Gambaudo, P. Hubert, P. Tisseur and S. Vaienti (eds.), World Scientific, 2000, 320 pp., price £ 59.-;
Level: advanced.
This volume starts interestingly with a 19-pages collection of problems in dynamical systems. There are 10 papers on smooth systems, 10 on symbolic dynamics and 7 papers on geometric systems mainly by European mathematicians.

  Time-dependent Partial Differential Equations and their Numerical Solution

Heinz-Otto Kreiss and Hedwig Ulmer Busenhart, Lecures in Mathematics ETH Zürich, Birkhäuser, 2001, 96 pp., price € 22.-
Level: introductory.
Easy-to-read introduction to hyperbolic and parabolic pde's with constant and with variable coefficients. It emphasizes the ideas while referring to the existing literature for more details. Attention is given to Cauchy problems, half-plane problems, difference methods and nonlinear cases.
  Adaptive Finite Element Methods for Differential Equations

Wolfgang Bangerth and Rolf Rannacher, Lectures in Mathematics ETH Zürich, Birkhäuser, 2003, 216 pp., price € 22.-
Level: introductory.
The emphasis is on Galerkin finite element methods with key issues error estimation and automatic mesh adaptation. The methods are discussed extensively and there are applications to eigenvalue problems, optimization, structural mechanics and fluid mechanics. With solutions of exercises.
  New Applications of Nonlinear and Chaotic Dynamics in Mechanics

Francis Moon (ed.), IUTAM Symposium, Kluwer Ac. Publ., 2002, 562 pp., price € 232.50
Level: introductory to medium.
Interesting collection of papers aimed at engineers with sections like analysis tools, bifurcation theory, elastica, cable sand shell dynamics, nonsmooth systems, vehicle and ship dynamics.
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