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數學
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10602幾何二

2017-09-01-2018-01-01

國立清華大學 數學系 宋瓊珠

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

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

 

幾何二學生筆記

前往課程 View Course
http://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=226&
https://www.youtube.com/watch?v=KzWRTQt0TOU&list=PLS0SUwlYe8cxLDo-7RMVD5K_LGTuhN9Zo