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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