國立清華大學數學系 教授
美國加州大學爾灣分校數學系 博士
| 【領域】 | 幾何分析、幾何、黎曼幾何、 微積分、偏微分方程導論 |
| 【專長】 | 微分幾何、幾何分析 |
授課老師
課程試聽
宋瓊珠 教授
最新消息
課程大綱
This is an introductory course on the theory of curves and surfaces in the three dimensional Euclidean space. After developing the theory of curves, we will study the geometry of a surface from both intrinsic and extrinsic point of view. Topics include first and second fundamental forms, various notions of curvature, and the famous Gauss-Bonnet theorem.
【課程簡述】
Brief course description
This is an introductory course on the theory of curves and surfaces in the three dimensional Euclidean space. After developing the theory of curves, we will study the geometry of a surface from both intrinsic and extrinsic point of view. Topics include first and second fundamental forms, various notions of curvature, and the famous Gauss-Bonnet theorem.
【課程說明】
Course Description
This is an introductory course on the theory of curves and surfaces in the three dimensional Euclidean space. After developing the theory of curves, we will study the geometry of a surface from both intrinsic and extrinsic point of view. Topics include first and second fundamental forms, various notions of curvature, and the famous Gauss-Bonnet theorem.
| ♠ | Prerequisites |
| Successful completion of Linear Algebra and Advanced Calculus |
【指定用書】
Text Books
| ♠ | Differential geometry of curves and surfaces, by Manfredo P. Do |
| Carmo. Prentice Hall. |
【參考書籍】
References
| ♠ | Elementary Differential Geometry, 2nd edition, A. Pressley, Springer, 2010. |
| ♠ | Elementary Differential Geometry, 2nd Edition, by Barrett O'Nell. |
【教學方式】
Teaching Method
| ♠ | Lectures. 講授，演習，討論. |
| www.math.nthu.edu.tw/~cjsung/course/ug2018s.html |
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回頂端第一講內容(OCW網站)=第1R講內容(Youtube網站)
- Geometry II
- The Sign of Gauss Curvature
- Geometric Interpretation of Gauss Curvature
- Vector Field
- Ruled Surface
- The Intrinsic Geometry of Surfaces: Fundamental Theorem of Surface
- Clairaut’s Theorem
- Hyperbolic Models
