The book provides a comprehensive introduction to the theory of ordinary differential equations at the graduate level and includes applications to Newtonian and Hamiltonian mechanics. It not only has a large number of examples and computer graphics, but also has a complete collection of proofs for the major theorems, ranging from the usual existence and uniqueness results to the Hartman-Grobman linearization theorem and the Jordan canonical form theorem. Maple's presence throughout the text blends traditional theory with new techniques made possible with a computer algebra system.

The book can be used almost exclusively in the traditional way for graduate math courses, or it can be used in an applied way for interdisciplinary courses involving physics, engineering, and other science majors. For this reason an extensive computer component using Maple is provided on Springer’s website.

This new edition has been extensively revised throughout, particularly the chapters on linear systems, stability theory and Hamiltonian systems.

The computer component is an in-depth supplement and complement to the material in the text and contains an introduction to discrete dynamical systems and iterated maps, special-purpose Maple code for animating phase portraits, stair diagrams, N-body motions, and rigid-body motions, and numerous tutorial Maple worksheets pertaining to all aspects of using Maple to study the topics in the text.