Ordinary differential equations with applications
Author(s)
Bibliographic Information
Ordinary differential equations with applications
（Texts in applied mathematics, 34）
Springer, c2006
2nd ed
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Note
Bibliography: p. [603]-618
Includes index
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Description and Table of Contents
Description
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 Contraction 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.
Table of Contents
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.
by "Nielsen BookData"