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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 on 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 and as a valuable resource for researchers.

This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.

Contents:

• Introduction
• 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
• Perturbation Methods
• Introduction to Monotone Dynamical Systems

Readership: Graduate students in mathematics, applied mathematics, and engineering.
Key Features:

• Comprehensively presents the theory of ordinary differential equations
• Many examples from mathematical models in physics and biology are presented to help the readers to understand the content of the theory and the applications in real world