TOCEC
數學,統計
層級: 課程資料
媒體: 影音 講義

10601幾何一

2017-02-01-2017-06-01

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

 

幾何一學生筆記

前往課程 View Course
http://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=205&
https://www.youtube.com/watch?v=v9M_JxoISI0&list=PLS0SUwlYe8cxMDB40oKDhLORWwvIRuUDO