This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.
Product Identifiers
Publisher
Atlantis Press (Zeger Karssen)
ISBN-13
9789462390201
eBay Product ID (ePID)
176912655
Product Key Features
Author
Thomas C. Sideris
Publication Name
Ordinary Differential Equations and Dynamical Systems
Format
Hardcover
Language
English
Subject
Mathematics
Publication Year
2013
Type
Textbook
Number of Pages
225 Pages
Dimensions
Item Height
235mm
Item Width
155mm
Volume
2
Item Weight
4853g
Additional Product Features
Title_Author
Thomas C. Sideris
Series Title
Atlantis Studies in Differential Equations
Country/Region of Manufacture
Netherlands
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