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Written in a straightforward and easily accessible style, this volume is suitable as a textbook for advanced undergraduate or first-year graduate students in mathematics, physical sciences, and engineering. The aim is to provide students with a strong background in the theories of Ordinary Differential Equations, Dynamical Systems and Boundary Value Problems, including regular and singular perturbations. It is also a valuable resource for researchers.

This volume presents an abundance of examples in physical and biological sciences, and engineering to illustrate the applications of the theorems in the text. Readers are introduced to some important theorems in Nonlinear Analysis, for example, Brouwer fixed point theorem and fundamental theorem of algebras. A chapter on Monotone Dynamical Systems takes care of the new developments in Ordinary Differential Equations and Dynamical Systems.

In this third edition, an introduction to Hamiltonian Systems is included to enhance and complete its coverage on Ordinary Differential Equations with applications in Mathematical Biology and Classical Mechanics.

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
• Introduction to Hamiltonian Systems

Readership: Advanced undergraduate and graduate students in mathematics, applied mathematics, physical sciences and engineering. Researchers in the fields of ordinary differential equations and dynamical systems.

Key Features:

• Besides giving rigorous proofs for basic theorems of ODE, it also provides numerous examples arising from physical and biological science for readers to understand the theorems and their applications
• Exercises are given at the end of each chapter for the reader to practice; some are challenging
• This is also a good textbook for students aiming for applied mathematics with applications in Engineering
• Some knowledge in Nonlinear Analysis in which we think is necessary for the students is presented in the book
• For oscillatory solutions which occur in nature, we introduce the Poincare–Bendixson Theorem and its applications, Monotone Dynamical Systems, especially three-dimensional competitive systems and Hopf bifurcations in n-dimensional space
• This text also provides a friendly introduction to Hamiltonian systems, written by co-author Kuo-Chang Chen, an expert in celestial mechanics

Ordinary Differential Equations with Applications