本教材共分為5章，具體介紹一階常微分方程初等解法，齊次線性微分方程一般解法、非齊次線性微分方程的常數(shù)變易法、非齊次線性微分方程伯努利方程解法，一階常微分方程積分因子求法以及四類隱式微分方程的解法，一階微分方程的解的存在性定理以及延拓性定理，高階微分方程的常數(shù)變易法以及非齊次（齊次）常系數(shù)高階微分方程的解法（待定系數(shù)法），變系數(shù)高階微分方程的解法，矩陣指數(shù)求法，一階線性微分方程組解的結(jié)構(gòu)以及解的存在性定理，非線性微分系統(tǒng)的穩(wěn)定性理論等知識(shí)點(diǎn)。
Chapter 1 Elementary Integration Methods
1.1 Differential equations and solutions
1.2 Variable separable equation
1.3 Homogeneous differential equations
1.4 First-order linear differential equations
1.5 Total differential equations and integration factors
1.6 First-order implicit differential equation
1.7 Several high-orderequations
Chapter 2 Fundamental Theorems.
2.1 Existence and uniqueness theorem
2.2 Theorem of existence and uniqueness of solution
2.3 Extension of the solution
2.4 Strange solution
2.5 Continuous dependence on initial value of the solution
Chapter 3 Linear Differential Equations
3.1 First order differential equations
3.2 General concepts of first-order linear differential equations
3.3 General theory of first-order linear homogeneous systems
3.4 General theory of first-order linear non-homogeneous systems
3.5 Solution of linear differential equations with constant coefficients
3.6 The solution method for linear differential equations(complex and multiple root)
Chapter 4 Linear Differential Equations
4.1 General theory of n-order linear differential equations
4.2 Solution of n-th order constant coefficient linear homogeneous equation
4.3 N-th order constant coefficient linear non-homogeneous equation solution
4.4 Second-order constant coefficient linear equations and vibration phenomena
Chapter 5 Introduction to Qualitative and Stability Theory
5.1 Concept of stability
5.2 Lyapunov's second method
5.3 Basic concepts of plane autonomous system
5.4 Introduction to plane qualitative theory
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