一般自然界的現象，我們常用微分方程的型式來模型化，例如在物理界，從牛頓的第二定律到近代的Maxwell 方程、 Einstein 的廣義相對論中的重力場方程和 Yang-Mills 場方程，還有物理量 (質量、動量、能量) 的守恒定律都可以用單一或一組方程式來表示；在生物界則有Lotka-Volterra 模型 (常微分方程組) 來表示 prey 和 predator 數量之間的關係。
基本課程包含：
- Intriduction: Some Basic Mathematical Models, Direction Fields; Solutions of Some Differential Equations; Classification of Differential Equations
- First Order Differential Equations: Linear Equations;Separable Equations; Modeling with First Order Equations; Differences Between Linear and Nonlinear Equations; Autonomous Equations and Population Dynamics; Exact Equations and Integrating Factors; Numerical Approximations, Euler Methods; The Existence and Uniqueness Theorem; First Order Difference Equations
- Second Order Linear Equations: Homogeneous Equations with Constant Coefficients; Fundamental Solution of Linear Homogeneous Equations; Linear Independence and the Wronskian; Nonhomogeneous Equations; Mechanical and Electrical Vibrations; Forced Vibrations
- Higher Order Linear Equations: General Theory of nth Order Linear Equations; The Methods of Undetermined Coefficients and Variation of Parameters
- Series Solutions of Second Order Linear Equations: Series Solutions of Euler Equations, Legendre Equation, , Chebyshev Equation and Bessel's Equations
- The Laplace Transform: Solution of Initial Value Problems; Differential Equations with Discontinuous
- System of First Order Linear Equations
- Boundary Value Problems
下學期若尚有剩餘的時間，則可能著重於下列專題:
- Nonlinear Differential Equations and Stability
- Partial Differential Equations and Fourier Series
- Numerical Methods
以下為常用之參考文獻：
- W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems
- F. John, Partial Differential Equations
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課程簡介 
