《常微分方程及其应用--理论与模型》是一本双语课教材。将常微分方程作为双语课，是因为学生不仅可以学到有关常微分方程、微积分和高等代数方面的专业术语，还可以通过不同领域的应用案例拓展阅读范围，从而提高学生的专业英语水平。为了使学生更好地理解和掌握学科知识，提高双语教学的教学质量和教学效果，书中对专业术语、比较难懂的词句作了注释。本书由周宇虹、罗建书编著。

《常微分方程及其应用--理论与模型》是常微分方程课程的英文教材，是作者结合多年的双语教学经验编写而成。全书共5章，包括一阶线性微分方程，高阶线性微分方程，线性微分方程组。Laplace变换及其在微分方程求解中的应用，以及微分方程的稳定性理论。书中配有大量的应用实例和用Matlab软件绘制的微分方程解的相图，并介绍了绘制相图的程序。

《常微分方程及其应用--理论与模型》可作为高等院校理工科偏理或非数学专业的本科双语教材，也可供相关专业的研究生、教师和广大科技人员参考。本书由周宇虹、罗建书编著。

Chapter 1 First.order Differential Equations

 1.1 Introduction

Exercise 1.1

 1.2 First—order Linear Differential Equations

 1.2.1 First—order Homogeneous Linear Differential Equations

 1.2.2 First—order Nonhomogeneous Linear Differential Equations

 1.2.3 Bernoulli Equations

Exercise 1.2

 1.3 Separable Equations

 1.3.1 Separable Equations

 1.3.2 Homogeneous Equations

Exercise 1.3

 1.4 Applications

 Module 1 The Spread of Technological Innovations

 Module 2 The Van Meegeren Art Forgeries

 1.5 Exact Equations

 1.5.1 Criterion for Exactness

 1.5.2 Integrating Factor

Exercise 1 5

 1.6 Existence and Uniqueness of Solutions

Exercise 1.6

Chapter 2 Second.order Differential Equations

 2.1 General Solutions of Homogeneous Second—order Linear Equations

Exercise 2.1

 2.2 Homogeneous Second—order Linear Equations with Constant Coeffcients

 2.2.1 The Characteristic Equation Has Distinct Real Roots

 2.2.2 The Characteristic Equation Has Repeated Roots

 2.2.3 The Characteristic Equation Has ComNeX Conjugate Roo~s

Exercise 2.2

 2.3 Nonhomogeneous Second—order Linear Equations

 2.3.1 Structure of General Solutions

 2.3.2 Method of Variation of Parameters

 2.3.3 Methods for Some Special Form of the Nonhomogeneous Term g(t)

Exercise 2.3

 2.4 Applications

 Module 1 An Atomic Waste Disposal Problem.

 Module 2 Mechanical Vibrations

Chapter 3 Linear Systems of Differential Equations

 3.1 Basic Concepts and Theorems

Exercise 3.1

 3.2 The Eigenvalue-Eigenvector Method of Finding Solutions

 3.2.1 The Characteristic Polynomial of A Has n Distinct Real

 Eigenvalues

 3.2.2 The Characteristic Polynomial of A Has Complex Eigenvalues

 3.2.3 The Characteristic Polynomial of A Has Equal Eigenvalues

Exercise 3.2

 3.3 YhndamentM Matrix Solution；Matrix—valued Exponential Function eAt

Exercise 3.3

 3.4 Nonhomogeneous Equations；Variation of Parameters

Exercise 3.4

 3.5 Applications

 Module 1 The Principle of Competitive Exclusion in Population Biology.

 Module 2 A Model for the Blood Glucose Regular System

Chapter 4 Laplace Transforms and Their Applications in Solving Differential Equations

 4.1 Laplace Transforms

Exercise 4.1

 4.2 Properties of Laplace Transforms

Exercise 4.2

 4.3 Inverse Laplace Transforms

Exercise 4.3

 4.4 Solving Differential Equations by Laplace Transforms

 4.4.1 The Right-Hand Side of the Differential Equation is Discontinuous

 4.4.2 The Right-Hand Side of Differential Equation is an Impulsive Function

Exercise 4.4

 4.5 Solving Systems of Differential Equations by Laplace Transforms

Exercise 4.5

Chapter 5 Introduction to the Stability Theory

 5.1 Introduction

Exercise 5.1

 5.2 Stability of the Solutions of Linear System

Exercise 5.2

 5.3 Geometrical Characteristics of Solutions of the System of Differential

 Equations

 5.3.1 Phase Space and Direction Field

 5.3.2 Geometric Characteristics of the Orbits near a Singular Point

 5.3.3 Stability of Singular Points

Exercise 5.3

 5.4 Applications

 Module 1 Volterra's Principle

 Module 2 Mathematical Theories of War

Answers to Selected Exercises

References

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