本課程是以微積分及線性代數的知識為基礎，介紹空間中之曲線與曲面的相關理論，以及它們的應用。主要的目的在於使同學瞭解如何掌握『彎曲』的概念，以及彎曲空間中 （正如我們所生存的地球）的幾何（例如什麼是『直線』等等）。為了深入探究這些數學理論，我們也將藉由較宏觀的角度，介紹整個幾何理論發展的歷史，使同學更進一步認識幾何學對於人類文明的影響，並瞭解我們所講授的課程內容在整體發展過程中的重要性。若時間許可，我們也將介紹近年來與幾何學相關的熱門應用--電腦輔助幾何設計（Computer Aided Geometric Design）的基本理論及結果。This course is based on the knowledge of micro points and linear generations, and introduces the correlation between curves and surfaces in space, as well as their applications. The main purpose is to enable students to understand how to master the concept of "王" and what is in the "王" space (like the earth where we live) (such as what is "王" and so on). In order to explore these mathematical theories in depth, we will also introduce the history of the development of the theory from a more macro perspective, so that students can further understand the impact of the theory on human civilization, and understand the importance of the course content we teach in the overall development process. If time permits, we will also introduce the basic theories and results of Computer Aided Geometric Design, a popular application related to learning in recent years.
教科書：
Theodore Shifrin, DIFFERENTIAL GEOMETRY: A First Course in Curves and Surfaces (Preliminary Version
Spring, 2013), University of Georgia.
（已獲作者同意，同學可至http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf或教學平台下載教材資料）
參考書籍/資料：
1. A. Pressley, Elementary Differential Geometry, Springer 2003.
2. Manfredo Do Carmo, Differential Geometry of Curves and Surfaces：Prentice Hall, 1976.
3. J. Gravesen, Differential Geometry and Design of Shape and Motion, Department of Mathematics
Technical University of Denmark 2002. (http://www2.mat.dtu.dk/people/J.Gravesen/cagd.pdf)
Textbook:
Theodore Shifrin, DIFFERENTIAL GEOMETRY: A First Course in Curves and Surfaces (Preliminary Version
Spring, 2013), University of Georgia.
(The author has been approved by the author. Students can download textbook materials at http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf or the teaching platform)
Reference books/data:
1. A. Pressley, Elementary Differential Geometry, Springer 2003.
2. Manfredo Do Carmo, Differential Geometry of Curves and Surfaces: Prentice Hall, 1976.
3. J. Gravesen, Differential Geometry and Design of Shape and Motion, Department of Mathematics
Technical University of Denmark 2002. (http://www2.mat.dtu.dk/people/J.Gravesen/cagd.pdf)
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 小考兩次小考兩次 Two small exams |
30 | |
| 期中考期中考 Midterm exam |
25 | |
| 期末考期末考 Final exam |
25 | |
| 平時成績平時成績 Regular achievements |
20 | 包括出席狀況、小小考、作業成績等等。 |
