Ordinary Differential Equations Introduction and Qualitative Theory

ISBN-10: 0824723376
ISBN-13: 9780824723378
Edition: 3rd 2011 (Revised)
List price: $115.95
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Description: Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Editionincludes basic material such as the existence and properties of solutions, linear equations,  More...

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Book details

List price: $115.95
Edition: 3rd
Copyright year: 2011
Publisher: CRC Press LLC
Publication date: 12/14/2007
Binding: Hardcover
Pages: 408
Size: 6.25" wide x 9.50" long x 1.00" tall
Weight: 1.540
Language: English

Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Editionincludes 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 ofperturbed 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.

Prefaces
Introduction
Existence Theorems
Linear Systems
Autonomous Systems
Stability
The Lyapunov Second Method
Periodic Solutions
Perturbation Theory: The Poincar� Method
Perturbation Theory: Autonomous Systems and Bifurcation Problems
Using the Averaging Method: An Introduction
Appendix
References
Index

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