Ordinary Differential Equations with Applications

✍ Scribed by Carmen Chicone (auth.)

• Publisher: Springer New York
• Year: 1999
• Tongue: English
• Leaves: 657
• Series: Texts in Applied Mathematics 34
• Edition: 2nd
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xv
Introduction to Ordinary Differential Equations....Pages 1-126
Linear Systems and Stability....Pages 127-197
Applications....Pages 199-282
Hyperbolic Theory....Pages 283-315
Continuation of Periodic Solutions....Pages 317-390
Homoclinic Orbits, Melnikov’s Method, and Chaos....Pages 391-450
Averaging....Pages 451-481
Local Bifurcation....Pages 483-529
Back Matter....Pages 531-561

✦ Subjects

Analysis