This new edition provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way (emphasis on the theory with the computer component as optional) or in a more applied way (emphasis on the applications and the computer material).

In this new edition, there are copious amounts of revisions and corrections, especially in the chapters on Linear Systems, Stability Theory, and Hamiltonian Systems.

"This book is intended for first- and second- year graduate students in mathematics and also organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering. ... The book is well written and provides many interesting examples. The author gives a comprehensive introduction to the theory on ordinary differential equations with a focus on mechanics and dynamical systems. The exposition is clear and easily understood. ... This book is accompanied with a CD-ROM to complement and supplement the material in the text." (Yuan Rong, Zentralblatt MATH, Vol. 993 (18), 2002)