During the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE).

This useful book, which is based around the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques.

Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook or as a valuable resource for researchers.

Contents:

• Fundamental Theory
• Linear Systems
• Stability of Nonlinear Systems
• Method of Lyapunov Functions
• Two-Dimensional Systems
• Second Order Linear Equations
• The Index Theory and Brouwer Degree
• Introduction to Perturbation Methods

“The book under review is a well-written textbook on ODE, suitable for advanced undergraduate or first year graduate students in Mathematics or Physical Sciences … The abundance of examples from physical and biological sciences and engineering to show the applications of the theorems presented in the text adds to the value of the book.”