Ordinary Differential Equations with Applications
(Sprache: Englisch)
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...
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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 Con traction 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.
Klappentext zu „Ordinary Differential Equations with Applications “
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.
Inhaltsverzeichnis zu „Ordinary Differential Equations with Applications “
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.
Bibliographische Angaben
- Autor: Carmen Chicone
- 2006, 2nd ed., 636 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 0387307699
- ISBN-13: 9780387307695
- Erscheinungsdatum: 18.05.2006
Sprache:
Englisch
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