本书是常微分方程课程的英文教材，由作者结合多年的全英文教学经验编写而成。主要内容包括常微分方程的初等积分法、线性微分方程组理论和常系数线性微分方程组的求解方法、高阶线性微分方程理论和常系数高阶线性微分方程的求解方法、解的存在唯一性理论、微分方程的定性理论以及常微分方程的数值求解方法等。为了读者更方便地运用Maple软件解决常微分方程的应用问题，本书给出了一些实际范例和Maple程序。
本书可作为高等学校数学与应用数学专业常微分方程课程的双语、全英文教材，也可供教师和科学技术人员参考。

Chapter 1 Elementary Integration Method
1.1 Fundamental Concepts
Exeraise 1.1
1.2 Separable Equations
Exercise 1.2
1.3 Homogeneous Equations
Exercise 1.3
1.4 First-Order Linear Differential Equations
Exercise 1.4
1.5 Exact Differential Equations
Exercise 1.5
1.6 Integrating Factor Method
Exercise 1.6
1.7 Flexibility in Problem Solving
Exercise 1.7
1.8 Implicit First-Order Differential Equations
Exercise 1.8
1.9 High-Order Differential Equations
Exercise 1.9
Chapter 2 Linear Systems of Differential Equations
2.1 First-Order System of Differential Equations
2.2 First-Order Linear System of Differential Equations
2.3 Existence and Uniqueness for First-Order System
Exercise 2.3
2.4 General Theory of Linear Homogeneous Systems
Exercise 2.4
2.5 General Theory of Nonhomogeneous Linear System
Exercise 2.5
2.6 Linear Differential System with Constant Coefficients
Exercise 2.6
2.7 Periodic Linear Systems
Exercise 2.7
Chapter 3 High-Order Linear Differential Equations
3.1 Introduction
Exercise 3.1
3.2 Existence and Uniqueness for High-Order Equations
Exercise 3.2
3.3 General Solutions of High-Order Homogeneous Linear Equations
Exercise 3.3
3.4 Nonhomogeneous High-Order Linear Differential Equations
Exercise 3.4
3.5 High-Order Homogeneous Linear Equations with Constant Coefficients
Exercise 3.5
3.6 High-Order Nonhomogeneous Linear Equations with Constant Coefficients
Exercise 3.6
3.7 Power Series Methods
Exercise 3.7
3.8 Laplace Transform Methods
Exeraise 3.8
Chapter 4 General Theory
4.1 Peano's Existence Theorem
Exercise 4.1
4.2 Existence and Uniqueness of Solutions
Exercise 4.2
4.3 Extension Theorem
Exercise 4.3
4.4 Continuous Dependence on Initial Values and Parameters
Exercise 4.4
Chapter 5 Qualitative Theory
5.1 Stability
Exercise 5.1
5.2 Stability of Linear Systems
Exercise 5.2
5.3 The Method of Lyapunov
Exercise 5.3
5.4 Basic Concepts of Two-Dimensional Autonomous Systems
Exercise 5.4
5.5 Critical Points of Two-Dimensional Linear Autonomous Systems
Exercise 5.5
5.6 Limit Cycles of Two-Dimensional Autonomous Systems
Exercise 5.6
Chapter 6 Numerical Methods for Ordinary Differential Equations
6.1 Introduction to Numerical Methods
6.2 Numerical Approximation: Euler's Method
6.3 An Improvement in Euler's Method
6.4 The Runge-Kutta Method
Appendix Application of Maple2020 for Ordinary Differential Equations
Al Introduction to Maple2020
A2 Basic Operations for Maple2020
A3 Maple2020 for Solving Ordinary Differential Equations
References