Differential Equations, Dynamical Systems, and an Introduction to Chaos M. W. Hirsch, S. Smale, and R. L. Devaney Elsevier-Academic Press (2004), price US $84.95, 425 pp. ISBN 0123497035.

This is the new edition of the classic text by Hirsch and Smale. Intended for the advanced undergraduate, the exposition is wonderfully readabable and contains from dynamical systems all the results which every student new to the subject should see; e.g., Smale's horseshoe map, the Lorenz attractor, an introduction to symbolic dynamics and the shift map, homoclinic bifurcations, etc.

The text is appropriate for students who have not had topology, and Chapters 9 through 17 would serve well for a follow-up course to differential equations; however, the text is self-contained with Chapters 1 through 8 presenting an excellent introduction to differential equations.

Any differential equations instructor should use this book as a reference for the class.