Ordinary Differential Equations with Applications

ISBN-10: 0387307699
ISBN-13: 9780387307695
Edition: 2nd 2006 (Revised)
Authors: Carmen Chicone
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Description: This book developed over 20 years of the author teaching the course at his own university. It serves as a text for a graduate level course in the theory of ordinary differential equations, written from a dynamical systems point of view. It contains  More...

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Book details

List price: $74.95
Edition: 2nd
Copyright year: 2006
Publisher: Springer
Publication date: 5/18/2006
Binding: Hardcover
Pages: 636
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 2.244
Language: English

This book developed over 20 years of the author teaching the course at his own university. It serves as a text for a graduate level course in the theory of ordinary differential equations, written from a dynamical systems point of view. It contains both theory and applications, with the applications interwoven with the theory throughout the text. The author also 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 second edition incorporates corrections and improvements of the original text. New material includes a proof of the Grobman-Hartman theorem for flows based on the Lie derivative, more extensive treatment of the Euler-Lagrange equation and its applications, a proof of Noether's theorem on the existence of first integrals in the presence of symmetries and a new section on dynamic bifurcation with a proof of Pontryagin's formula.  The impressive array of existing exercises has been more than doubled in size and further enhanced in scope, providing mathematics, physical science and engineering graduate students with a thorough introduction to the theory and application of ordinary differential equations. Reviews of the first edition: ``As an applied mathematics text on linear and nonlinear equations, the book by Chicone is written with stimulating enthusiasm. It will certainly appeal to many students and researchers.'' -- F. Verhulst, SIAM Review ``The author writes lucidly and in an engaging conversational style. His book is wide-ranging in its subject matter, thorough in its presentation, and written at a generally high level of generality, detail, and rigor.'' -- D. S. Shafer, Mathematical Reviews

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

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