基本素養 Basic Literacy
無核心能力 Competence
■ 掌握連續與逼進的能力
Ability to handle continuity phenomena and approximations.
□ 處理數字及符號運算的能力
Ability to operate with symbols and digits.
□ 透視形像與空間的能力
Ability to visualize space, shape, and images.
□ 利用計算機處理數學的能力
Ability of computer to do mathematics.
□ 應用隨機理論的能力
Ability to apply stochastic mathematics.
□ 處理大量數據的能力
Ability to handle large amount of data.
□ 處理離散型數學的能力
Ability to do mathematics relating to discrete models.
□ 獨立研究與撰寫論文的能力
Ability to do independent researches and to write thesis.
□ 使用計算機的能力
Abilities to use computer as a tool.
課程概述 Course Description
本課程學習偏微分方程的概念與基本類型以及它們的屬性。討論邊界問題，傅立葉級數，調和函數。研究Green等式和Green函數，在空間的波，在空間及平面的邊界，一般特徵值問題，與波分佈的想法。We study the concepts and basic types of PDE, and their properties. Then we discuss boundary problems, Fourier Series, and Harmonic Funtions. Next we investigate the ideas of Green`s Identities and Green`s Functions, Waves in Space, Boundaries in the Plane and in Space, General Eigenvalue Problems, and Distributions.
課程學習目標 Course Objectives
課程進度 Course Outline
| 週次 Week | 進度說明 Progress Description |
|---|---|
| 1 | Where PDEs Come From |
| 2 | Where PDEs Come From |
| 3 | Waves and Diffusions |
| 4 | Waves and Diffusions |
| 5 | Reflections and Sources |
| 6 | Reflections and Sources |
| 7 | Boundary Problems |
| 8 | Boundary Problems |
| 9 | Boundary Problems |
| 10 | Fourier Series |
| 11 | Fourier Series |
| 12 | Fourier Series |
| 13 | Harmonic Functions |
| 14 | Harmonic Functions |
| 15 | Green`s Identities and Green`s Functions |
| 16 | Green`s Identities and Green`s Functions |
| 17 | Waves in Space |
| 18 | Waves in Space |
以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.
有關課程其他調查 Other Surveys of Courses
1.本課程是否規劃業界教師參與教學或演講?Is there any industry specialist invited in this course? How many times?
2.本課程是否規劃含校外實習(並非參訪)? 否
Are there any internships involved in the course? How many hours? No
3.本課程是否可歸認為學術倫理課程?
Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics?
4.本課程是否屬進入社區實踐課程?
Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?