Chapter 1 Introduction 1.1 Ordinary Differential Equation Models 1.2 Basic Concepts Chapter 2 First Order Differential Equations 2.1 Separable Equations 2.2 First Order Linear Equations 2.3 Exact Equations and Integrating Factors 2.4 Implicit First Order Differential Equations 2.5 Applications of First Order Equations Chapter 3 Fundamental Theory of the First Order Differential Equations 3.1 The Existence and Uniqueness Theorem 3.2 Extension of Solutions 3.3 Continuous Dependence and Differentiability of Solutions with Respect to Initial Values Chapter 4 Higher Order Linear Differential Equations 4.1 General Theory of nth Order Linear Differential Equations 4.2 Linear Differential Equations with Constant Coefficients 4.3 Reduction of Order 4.4 The Laplace Transform Chapter 5 Systems of First Order Linear Differential Equations 5.1 The Concepts of Systems of Ordinary Differential Equations 5.2 Basic Theory of Systems of Linear Equations 5.3 Linear Systems with Constant Coefficients Chapter 6 Nonlinear Differential Equations and Stability 6.1 Stability 6.2 The Method of Lyapunov 6.3 Stability Analysis of Two Biological Models References
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