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層級課程資料
媒體類型影音課程
講義課程
標題幾何一
授課教師國立清華大學 宋瓊珠
授課日期2017-02(起) 2017-06(迄)
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
學習型式課程
分類號與分類名稱310 數學
摘要課程大綱
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.
指定用書】
Text Books
*
Differential geometry of curves and surfaces, by Manfredo P. Do Carmo.Prentice Hall,
*
Elementary Differential Geometry, 2nd edition, A. Pressley, Springer, 2010. 



【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
網址http://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=205&

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