微分方程式是建立數學模型時的主要工具之一，微分方程的解法，無論是理論方法或數值方法，都廣泛地被應用在物理、氣象、工程、經濟、財務、生物醫學等領域。單一自變數的微分方程通稱作常微分方程、而二個（含）以上自變數的微分方程通稱作偏微分方程。本課程只聚焦在常微分方程的理論與解法。課程目標如下：
0.以實例學習如何為現象建立常微分方程的數學模型。
1.學習常微分方程的分類方式。
2.學習單一常微分方程式的理論與解法。
3.學習線性微分方程式（組）解的行為與理論解法。
4.學習分析非線性常微分方程式（組）解的行為，與數值解法。

Differential equations are one of the main tools for establishing mathematical models. Solutions to differential equations, whether theoretical or numerical, are widely used in physics, meteorology, engineering, economics, finance, biomedicine and other fields. Differential equations with a single independent variable are generally called ordinary differential equations, while differential equations with two or more independent variables are generally called partial differential equations. This course only focuses on the theory and solutions of ordinary differential equations. The course objectives are as follows:
0. Learn how to establish mathematical models of ordinary differential equations for phenomena through examples.
1. Learn how to classify ordinary differential equations.
2. Learn the theory and solution of a single ordinary differential equation.
3. Learn the behavior and theoretical solution methods of linear differential equations (groups).
4. Learn to analyze the behavior of solutions to nonlinear ordinary differential equations (groups) and numerical solution methods.

1. R. K. Nagle, E. B. Saff, and A . D. Snider, Fundamentals of Differential Equations, 6 Ed. Pearson.
2. E. Rainville, P. Bedient, R. Bedient, Elementary Differential Equations 8/E, Pearson

1. R. K. Nagle, E. B. Saff, and A. D. Snider, Fundamentals of Differential Equations, 6 Ed. Pearson.
2. E. Rainville, P. Bedient, R. Bedient, Elementary Differential Equations 8/E, Pearson