Ordinary Differential Equations: Basics and Beyond

• Main Authors: Schaeffer, David G. (Author), Cain, John W. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2016.
• Series: Texts in Applied Mathematics, 65
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Physics.; Ordinary Differential Equations.; Theoretical, Mathematical and Computational Physics.; Dynamical Systems and Ergodic Theory.

This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposi...

Table of Contents:

• Introduction
• Linear Systems with Constant Coefficients
• Nonlinear Systems: Local Theory
• Nonlinear Systems: Global Theory
• Nondimensionalization and Scaling
• Trajectories Near Equilibria
• Oscillations in ODEs
• Bifurcation from Equilibria
• Examples of Global Bifurcation
• Epilogue
• Appendices.