This book is developed primarily from the author's 20 years of teaching the course at his own university. It addresses both theory and applications, interweaving application with theory throughout the text. The author links ordinary differential equations with advanced mathematical topics such as differential geometry, Lie group theory, analysis in infinite-dimensional spaces and even abstract algebra. The revised edition includes considerable new material; the impressive array of exercises has been more than doubled in size and enhanced in scope.

Klappentext

Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions.

Inhalt

to Ordinary Differential Equations.- Linear Systems and Stability.- Applications.- Hyperbolic Theory.- Continuation of Periodic Solutions.- Homoclinic Orbits, Melnikov's Method, and Chaos.- Averaging.- Local Bifurcation.