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 when establishing mathematical models. The solutions to differential equations, whether they are theoretical methods or numerical methods, are widely used in fields such as physics, atmosphere, engineering, economy, finance, and biological medicine. Differential equations of a single autovariable are generally called ordinary differential equations, while differential equations of two (including) or more autovariables are generally called partial differential equations. This course only focuses on the theory and solutions of ordinary differential equations. The course goals are as follows:
0. Use examples to learn how to establish a mathematical model of ordinary differential equations for phenomena.
1. Learn how to classify ordinary differential equations.
2. Learn the theory and solutions of single ordinary differential equations.
3. Learn the behavior and theoretical solutions of the solution of linear differential equations (assembly).
4. Learn and analyze the behavior of solutions of nonlinear ordinary differential equations (assembly) and numerical solutions.
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
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 作業作業 Action |
30 | 每週依教學進度指派習題，繳交後由教師給成績 |
| 考試考試 exam |
70 | 預計有二次小考、期中考、期末考，以上每次35% |
