本課程是數學建模(mathematical modeling)的入門課程。主要目標是學習如何將由物理學、化學、生物學與社會科學領域產生的問題，描寫成數學方程式，以數學進行研究。一般而言，這是不容易的，這同時需要對產生問題的領域與數學都有瞭解。本課程的重點，在於透過學習幾個經典的例子，理解數學建模的過程與方程式背後的觀念。相對而言，方程式背後的數學理論與數值模擬，將在其他課程(如微分方程、數值分析)中有詳細的說明。除了教師授課，將安排一至兩次上課時間讓同學以數學軟體(Mathematica或Matlab)進行電腦實習。
This course is an entry-level course for mathematical modeling. The main goal is to learn how to describe the problems arising from the fields of physics, chemistry, biology and social sciences into mathematical equations for research in mathematics. Generally speaking, this is not easy, and at the same time, you need to have an understanding of the domain and mathematics that arise. The focus of this course is to understand the concepts behind mathematical modeling processes and equations through learning a few classic examples. Relatively speaking, the mathematical theory and numerical simula behind the equation will be explained in detail in other courses (such as differential equations and numerical analysis). In addition to teacher teaching, one to two class sessions will be arranged for students to practice computers with mathematical software (Mathematica or Matlab).
1. Giordano, Frank R., Fox, William P., & Horton, Steven B (2014), A First Course in Mathematical Modeling 5th ed. Boston, MA: Brooks/Cole, Cengage Learning.
2. M. Endo, T. Kitabayashi (2017), Differential Equations and Modeling of Physical Systems－How a mathematical model of phenomenon is built? Shokabo, Tokyo.
3. K. Tung (2007), Topics in mathematical modelling, Princeton University Press.
4. 其他補充教材
1. Giordano, Frank R., Fox, William P., & Horton, Steven B (2014), A First Course in Mathematic Modeling 5th ed. Boston, MA: Brooks/Cole, Cengage Learning.
2. M. Endo, T. Kitabayashi (2017), Differential Equations and Modeling of Physical Systems-How a mathematical model of phenomenon is built? Shokabo, Tokyo.
3. K. Tung (2007), Topics in mathematical modelling, Princeton University Press.
4. Other supplementary textbooks
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 作業作業 Action |
40 | |
| 期中考期中考 Midterm exam |
20 | |
| 期末報告期末報告 Final report |
40 |
