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層級課程資料
媒體類型影音課程
講義課程
標題幾何二
授課教師國立清華大學 宋瓊珠
授課日期2017-09(起) 2018-01(迄)
關鍵字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
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.


【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
網址http://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=226&

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