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 introductory course in mathematical modeling. The main goal is to learn how to describe problems arising in the fields of physics, chemistry, biology and social sciences into mathematical equations and to study them mathematically. Generally speaking, this is not easy and requires an understanding of both the domain in question and the mathematics. The focus of this course is to understand the process of mathematical modeling and the concepts behind equations through studying several classic examples. Relatively speaking, the mathematical theory and numerical simulation behind the equations will be explained in detail in other courses (such as differential equations, numerical analysis). In addition to lectures by teachers, one or two class periods will be arranged for students to practice computer practice using 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 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 modeling, Princeton University Press.
4. Other supplementary teaching materials
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 作業作業 Homework |
40 | |
| 期中考期中考 midterm exam |
20 | |
| 期末報告期末報告 Final report |
40 |
