Differential Equations: Theory and Applications

• Main Author: Betounes, David. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Subjects: Mathematics.; Differentiable dynamical systems.; Differential Equations.; Numerical analysis.; Mathematical physics.; Ordinary Differential Equations.; Numerical Analysis.; Dynamical Systems and Ergodic Theory.; Mathematical Methods in Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4419-1163-6

The book provides a comprehensive introduction to the theory of ordinary differential equations at the graduate level and includes applications to Newtonian and Hamiltonian mechanics. It not only has a large number of examples and computer graphics, but also has a complete collection of proofs for t...

Table of Contents:

• Introduction
• Techniques, Concepts and Examples
• Existence and Uniqueness: The Flow Map.-Linear Systems
• Linearization and Transformation
• Stability Theory
• Integrable Systems
• Newtonian Mechanics.-Hamiltonian Systems
• Appendix A: Elementary Analysis
• Appendix B: Lipschitz Maps and Linearization
• Appendix C: Linear Algebra.-Appendix D: Electronic Contents.