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Bibliographic Details

Title: Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition (Chapman & Hall/CRC Pure and Applied Mathematics)
Publisher: CRC Press
Publication Date: 2007
Language: English
ISBN 10: 0824723376
ISBN 13: 9780824723378
Binding: hardcover
Edition: 3rd Edition
Condition: Good

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Synopsis

Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of nonlinear equations. Requiring only a background in advanced calculus and linear algebra, the text is appropriate for advanced undergraduate and graduate students in mathematics, engineering, physics, chemistry, or biology.

This third edition of a highly acclaimed textbook provides a detailed account of the Bendixson theory of solutions of two-dimensional nonlinear autonomous equations, which is a classical subject that has become more prominent in recent biological applications. By using the Poincar� method, it gives a unified treatment of the periodic solutions of perturbed equations. This includes the existence and stability of periodic solutions of perturbed nonautonomous and autonomous equations (bifurcation theory). The text shows how topological degree can be applied to extend the results. It also explains that using the averaging method to seek such periodic solutions is a special case of the use of the Poincar� method.