10602 自然科學學群 數學系

幾何二

宋瓊珠 教授

數學系
國立清華大學數學系       教授 
美國加州大學爾灣分校數學系      博士

【領域】 幾何分析、幾何、黎曼幾何、 微積分、偏微分方程導論
【專長】 微分幾何、幾何分析

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Syllabus

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. 
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

 

Keyword

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

Teachers

宋瓊珠 教授

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