This course aims to give a college-level science students how to use differential equations to facilitate the scientific research. The students will learn the usage of mathematical model to distill theories from empirical data and to quantify the theories with a set of governing mathematical equations.

課程討論如何以數學模式強化科學研究。學生學習數學模式協助從資料建立理論，以及對理論的數量化。課程將重視微分方程的數學建模，重視方程式的科學意義詮釋與分析，課程也將討論微分方程式的解析解與計算解。課程元素亦將介紹大氣科學、流體力學以及生態、生命科學等模式建立例子。
課程之內容如下，一些特殊課題視學生需求選擇授課
1. Calculus—the Mathematics of Change
2. Commonly Occurring Functions
3. Introduction to Dynamic Modeling
4. Equilibriums and Stabilities
5. Phase Plane and Intuitive Approach
6. Equations of Exponential and Periodic Solutions
7. e-1 scale, Residence Time, and Relaxation
8. Dating Games and the HIV problem
9. Feedback, Fast and Slow Scales,
10. Nonlinear Dynamic Modeling
11. Nonlinear Dynamical Model Examples
12. Writing the Equations of Marriage Model
13. Synchronization Examples
14. Chaos and Catastrophic Change Examples
15. Dimensional Analysis
16. Examples in Dimensional Analysis
17. Multiple Scale Phenomena and Non-dimensional Parameters
18. Perturbation Multiple Scale Analysis
19. Lavi-Civita Symbol
20. Fourier analysis and Integral Transform
21. Partial Differential Equations
22. Spectral Method
23. Convolution and deconvolution
24. Calculus of Variation