微分流形（英）（2016 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 (12/13) Final Exam: Jan. 9, 7pm-9pm @ 5104.

o (12/26) Lecture 25 uploaded.

o (12/30) Lecture 26 uploaded.

o (12/30) PSet 7 uploaded. Not to be turned in.

o (12/30) Office Hour: Jan 4, 2:00-4:00 @ 1601.

o (1/4) Solution to PSet 6 uploaded (prepared by TA).

o (1/4) TA will take the last PSet to classroom on Jan. 5 at 2pm.

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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：   星期一下午 2：00pm – 3：35pm; 星期五下午 2：00pm – 3：35pm; 　

o 上课地点：   五教 5104

o 办公室：   管研楼1601

o 助教：   马翘楚 ( at mail dot ustc dot edu dot cn)

o 答疑时间：   TBA

o 答疑地点：   TBA

o 参考书籍   John Lee, Introduction to Smooth Manifolds

o 参考书籍   Loring Tu, An Introduction to Manifolds

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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。

序号 日期 内容 讲义 作业
  Lecture 1     09/12     Review of Topology, Topological Manifolds     Lect 1     PSet 1   : Due Oct. 10.
  Lecture 2     09/18     Review of Analysis, Smooth Manifolds     Lect 2  
  Lecture 3     09/19     Smooth Functions, Partition of Unity     Lect 3  
  Lecture 4     09/23     Smooth Maps, Tangent Vectors     Lect 4  
  Lecture 5     09/26     Differentials, Immersions and Submersions     Lect 5     PSet 2   : Due Oct. 24.
  Lecture 6     10/9     Smooth Submanifolds     Lect 6  
  Lecture 7     10/10     Transversality, Morse Functions     Lect 7  
  Lecture 8     10/14     Sard's Theorem, The Whitney Embedding Theorem     Lect 8  
  Lecture 9     10/17     Vector Bundles, Vector Fields     Lect 9     PSet 3   : Due Nov. 7.
  Lecture 10     10/21     Integral Curves, Flows     Lect 10  
  Lecture 11     10/24     Distributions, The Frobenius Theorem     Lect 11  
  Lecture 12     10/28     Lie Groups and Lie Algebras     Lect 12  
  Lecture 13     10/31     Exponential Map, Lie Subgroups     Lect 13     PSet 4   : Due Nov. 21.
      11/4     Cancelled: Sports Meeting      
  Lecture 14     11/7     Lie Group Actions     Lect 14  
  Lecture 15     11/11     Fiber Bundles, Principal Bundles     Lect 15  
      11/14     Problem Session by TA      
      11/18     Midterm: Cover Lecture 1-14      
  Lecture 16     11/21     Multilinear Algebra     Lect 16     PSet 5   : Due Dec. 12.
  Lecture 17     11/25     Differential Forms     Lect 17  
  Lecture 18     11/28     Integration of differential forms     Lect 18  
  Lecture 19     12/2     The de Rham Cohomology     Lect 19     PSet 6   : Due Dec. 26.Sol
  Lecture 20     12/5     The Mayer-Vietoris Sequence     Lect 20  
  Lecture 21     12/9     The de Rham Cohomology with Compact Supports     Lect 21  
  Lecture 22     12/12     Mapping Degree Theory, The Poincare Duality     Lect 22  
  Lecture 23     12/16     Symplectic Manifolds     Lect 23     PSet 7   : Not to be turned in.
  Lecture 24     12/18     Moser's Trick, The Darboux Theorem     Lect 24  
      12/23     Problem Session by TA      
  Lecture 25     12/26     Connections and Curvatures     Lect 25  
  Lecture 26     12/30     The Chern-Weil Theory     Lect 26  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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