微分流形（2021 秋季学期）


中国科学技术大学数学科学学院

[课程公告] [课程信息] [课程安排，讲义以及习题]

课程公告

o (12/14) No class on Dec. 23. Classes on Dec. 16 and Dec. 30 will be extended by 45 minutes each.

o (12/16) Projects for A+ uploaded. [Prerequirement: Midterm at least 119 ]

o (12/16) Lecture 25 uploaded.

o (12/16) PSet 7，part 2 uploaded. Due: Dec. 28.

o (12/16) Final Exam: Jan. 06, 16:00-18:00 @ 5303 Cover Lecture 1 - Lecture 28.

o (12/23) Lecture 26 uploaded.

o (12/23) PSet 8，part 1 uploaded. Due: Jan. 4.

o (12/28) Lecture 27 uploaded.

o (12/31) Lecture 28 uploaded.

o (12/31) PSet 8，part 2 uploaded. Due: Jan. 4.

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课程信息

o 授课老师：   王作勤 (wangzuoq at ustc dot edu dot cn)

o 上课时间：   星期二上午 07：50 – 09：25; 星期四下午 15：55 – 17：30; 　

o 上课地点：   一教 1102

o 办公室：   管研楼1601

o 助教：   HONG Fang （hongf at mail dot ustc dot edu dot cn） HUANG Shuping (hsp at mail dot ustc dot edu dot cn) CHEN Hengyu (hichychen at mail dot ustc dot edu dot cn)

o 答疑时间：   Saturday, 9:30-11:30

o 答疑地点：   5103

o 参考书籍   John Lee, Introduction to Smooth Manifolds (Second Edition)

o 参考书籍   Loring Tu, An Introduction to Manifolds

o 参考书籍   Victor Guillemin and Alan Pollack, Differential Topology

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课程安排，讲义以及习题

o 课程安排可能会随着课程的进行而略有变动。

o 课程的讲义将在每堂课后上传。

o 作业在标明的日期(通常是周二)课前交。

序号 日期 内容 讲义 作业
  Lecture 1     09/14     Review of Topology, Topological Manifolds     Lect 1     PSet 1, Part1   : Due Sep. 28.
  Lecture 2     09/16     Smooth Manifolds     Lect 2  
  Lecture 3     09/23     Smooth Functions, Partition of Unity     Lect 3     PSet 1, Part2   : Due Sep. 28.
  Lecture 4     09/28     Smooth Maps     Lect 4     PSet 2, Part 1   : Due Oct. 14.
  Lecture 5     09/30     The Differential     Lect 5  
  Lecture 6     10/09     Local Behavior via the Differential     Lect 6     PSet 2, Part 2   : Due Oct. 14.
  Lecture 7     10/12     Sard's Theorem     Lect 7     PSet 3, Part 1   : Due Oct. 28.
  Lecture 8     10/14     Smooth Submanifolds     Lect 8  
  Lecture 9     10/19     The Whitney Embedding Theorem     Lect 9     PSet 3, Part 2   : Due Oct. 28.
  Lecture 10     10/21     Tubular Neighborhood Theorem     Lect 10  
  Lecture 11     10/26     Smooth Approximations and Smooth Deformations     Lect 11     PSet 4, Part 1   : Due Nov. 11.
  Lecture 12     10/28     Transversality     Lect 12  
  Lecture 13     11/02     Smooth Vector Fields     Lect 13     PSet 4, Part 2   : Due Nov. 11.
  Lecture 14     11/04     Integral Curves of Vector Fields     Lect 14  
  Lecture 15     11/09     The dynamical system associated with a vector field     Lect 15     PSet 5, Part 1   : Due Nov. 25.
  Lecture 16     11/11     Distributions and foliations     Lect 16  
  Lecture 17     11/16     Lie groups and Lie algebras     Lect 17     PSet 5, Part 2   : Due Nov. 25.
  Lecture 18     11/18     The exponential map     Lect 18  
  Lecture 19     11/23     Lie subgroups     Lect 19     PSet 6, Part 1   : Due Dec. 9.
  Lecture 20     11/25     Lie group actions     Lect 20  
      11/30     考前答疑  
      12/01     Midterm 16:00-18:00 @ 5202 Cover: Lec 1 - Lec 18.  
  Lecture 21     12/02     Tensors and k-forms     Lect 21     PSet 6, Part 2   : Due Dec. 9.
  Lecture 22     12/07     The exterior derivative     Lect 22     PSet 7, Part 1   : Due Dec. 28.
  Lecture 23     12/09     Integration on manifolds     Lect 23  
  Lecture 24     12/14     The Stokes' formula     Lect 24     PSet 7, Part 2   : Due Dec. 28.
  Lecture 25     12/16 (extended)     The De Rham Cohomology     Lect 25  
  Lecture 26     12/21     The Mayer-Vietoris sequence     Lect 26     PSet 8, Part 1   : Due Jan. 04.
      12/23 (canceled)     No class.      
  Lecture 27     12/28     Compactly supported De Rham Cohomology     Lect 27     PSet 8, Part 2   : Due Jan. 04.
  Lecture 28     12/30 (extended)     Applications of de Rham Theory     Lect 28  
      01/04     考前答疑         Projects for A+ candidates   : Due Jan. 8.
      01/06     Final Exam 16:00-18:00 @ 5303 Cover: Lec 1 - Lec 28.      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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