Chicone Ordinary Differential Equations with Applications

Third Auflage 2024
ISBN: 978-3-031-51652-8
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 34, 729 Seiten, eBook

Reihe: Texts in Applied Mathematics

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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Chicone, Carmen

Inhaltsverzeichnis

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.

Über Autor(innen)

Carmen Chicone is an emeritus professor of mathematics at the University of Missouri. He has authored two books, coauthored a third, and published over 100 research articles. His recent research interests are in the qualitative theory of ordinary and partial differential equations, applications of differential equations to mathematical models in science and engineering, and the development of numerical methods to obtain viable predictions from physically realistic model problems.