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數學,統計
| 層級： | 課程資料 |
| 媒體： | 影音 講義 |
10601幾何一Geometry I
2017-02-01-2030-12-30
國立清華大學 數學系 宋瓊珠
關鍵字： Geometry I Parametrized Curves Space Curves: Moving Frames and Torsion Global property of plane curves Regular surface The Tangent Plane; the Differential of a Map Orientation of Surfaces The Geometry of the Gauss Map Geometry of the Gauss Map Gauss Curvature in Local Coordinates
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. ♠ Prerequisites Successful completion of Linear Algebra and Advanced Calculus
指定用書Text Books
♠ Elementary Differential Geometry, 2nd edition, A. Pressley, Springer, 2010. ♠ Differential geometry of curves and surfaces, by Manfredo P. Do Carmo .Prentice Hall, 1976.
參考書籍References
♠ Elementary Differential Geometry, 2nd Edition, by Barrett O'Nell.
教學方式 Teaching Method ♠ Lectures、講授、演習、討論
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
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.
| ♠ | Prerequisites |
| Successful completion of Linear Algebra and Advanced Calculus |
指定用書
Text Books
| ♠ | Elementary Differential Geometry, 2nd edition, A. Pressley, Springer, 2010. |
| ♠ | Differential geometry of curves and surfaces, by Manfredo P. Do Carmo |
| .Prentice Hall, 1976. | |
參考書籍
References
| ♠ | Elementary Differential Geometry, 2nd Edition, by Barrett O'Nell. |
教學方式
Teaching Method
| ♠ | Lectures、講授、演習、討論 |
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http://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=205&
https://www.youtube.com/watch?v=v9M_JxoISI0&list=PLS0SUwlYe8cxMDB40oKDhLORWwvIRuUDO