常微分方程

《常微分方程（英文版）》主要介紹了常微分方程的相關知識，內容包括一階線性微分方程、存在性定理、高階微分方程定理、微分方程組、穩定性等。為了便於學生更好地掌握，書中列舉了大量的典型例題，且大部分章節後面配有對應的習題，學生可以更好地檢驗自己對相關知識的掌握程度。

Chapter 1 Introduction

1．1 Differential Equations and Mathematical Models

1．2 Basic Concept

1．3 Direction Fields

Chapter 2 First-Order Differential Equations

2．1 Introduction： Motion of a Falling Body

2．2 Separable Equations

2．3 Linear Equations

2．4 Exact Equations

2．5 Special Integrating Factors

2．6 Substitutions and Transformations

Chapter 3 Existence and Uniqueness Theory

3．1 Picard's Existence and Uniqueness Theorem

3．2 Existence of Solutions of Linear Equation

3．3 Estimates of Error and Approximate Calculation

3．4 Continuation of Solutions

3．5 Continuous Dependence of Solutions

Chapter 4 Theory of Higher-Order Linear Differential Equations

4．1 Basic Theory of Linear Differential Equations

4．2 Homogeneous Linear Equations with Constant Coefficients

4．3 Undetermined Coefficients and the Annihilator Method

4．4 Method of Variation of Parameters

4．5 Cauchy-Euler Equation

4．6 Solution by Power Series

4．7 Laplace Transforms

Chapter 5 Systems of Differential Equations

5．1 Introduction

5．2 Existence and Uniqueness Theorem for Linear Systems

5．3 Properties of Solutions of First-Order Linear Systems

5．4 Homogeneous Linear Systems with Constant Coefficients

5．5 Complex Eigenvalues

5．6 The Matrix Exponential Function

5．7 Nonhomogeneous Linear Systems

Chapter 6 Stability

6．1 Introduction

6．2 Linear Systems in the Plane

6．3 Almost Linear Systems

6．4 Lyapunov's Direct Method

Chapter 7 Fractional Differential Equations

7．1 Riemann-Liouville Integrals

7．2 Riemann-Liouville Derivatives

7．3 Relations between Riemann-Liouville Integrals and Derivatives

7．4 Caputo's Derivative

7．5 Existence and Uniqueness Results for Riemann-Liouville Fractional Differential Equations

7．6 Existence and Uniqueness Results for Caputo Fractional Differential Equations

Chapter 8 Dynamic Equations on Time Scales

8．1 Basic Definitions

8．2 Differentiation

8．3 Integration

References