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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