Ordinary Differential Equations: Introduction And Qualitative Theory - Couverture rigide

Cronin, Jane

Couverture rigide

ISBN 10 : 0824723376 ISBN 13 : 9780824723378

Editeur : CRC Press Inc, 2007

Synopsis

Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition provides a detailed account, based on the work of Lefschetz, of the Bendixson theory of solutions of two-dimensional autonomous systems in a neighborhood of a singular point. Updated and revised, this third edition presents a unified treatment of the perturbation problem for periodic solutions, covering nonautonomous equations and bifurcation problems. The text includes a self-contained account of topological degree and its use as well as a detailed description of how the averaging method can be used to examine the problem of periodic solutions. It also contains additional exercises, applications, and solutions.

A propos du livre

Présentation de l'éditeur

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 Poincaré 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 Poincaré method.

Détails de l'édition

• Éditeur: CRC Press Inc
• Date d'édition: 2007
• ISBN 10: 0824723376
• ISBN 13: 9780824723378
• Reliure: Relié
• Langue: anglais
• Numéro d'édition: 3
• Nombre de pages: 408