泛函分析（H）（英）（2015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 (12/30) Typed Lecture 19 uploaded.

o (12/30) Typed Lecture 23 uploaded.

o (12/30) Typed Lecture 25 uploaded.

o (12/30) Typed Lecture 26 uploaded.

o (12/30) No class on Jan. 5. Exercise Class on Jan. 8th by TA.

o (1/8) Typed Lecture 20 uploaded.

o (1/8) Typed Lecture 21 uploaded.

o (1/8) Typed Lecture 22 uploaded.

o (1/12) Typed Lecture 24 uploaded.

o (12/16) Final Exam: 2016-01-15, 14:30--16:30 @ 3C121

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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 9：45am – 11：20am; 星期五上午 7：50am – 9：25am　

o 上课地点：   教三楼 3A405

o 办公室：   管研楼1601

o 助教：   程怡然 (story at mail dot ustc dot edu dot cn)

o 答疑时间：   星期六晚上 7:30pm - 9:00pm

o 答疑地点：   教三楼 3A309

o 教材   Walter Rudin，泛函分析（英文版，第二版）

o 参考书籍   Peter Lax, Functional Analysis

o 参考书籍   Michael Reed and Barry Simon, Methods of Modern Mathematical Physics Vol. 1:　Functional Analysis

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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 作业在每周二课前交。

序号 日期 内容 讲义 作业 测验
  Lecture 1     09/01     Introduction; Vector spaces; Metric     Lect 1     PSet 1, part 1   : Due Sep. 8.
  Lecture 2     09/06     Convergence, Completeness of metric spaces     Lect 2     PSet 1, part 2   : Due Sep. 8.
  Lecture 3     09/08     Metric topology, Baire's category theorem     Lect 3     PSet 2, part 1   : Due Sep. 15.
  Lecture 4     09/11     Topology, Topological vector spaces     Lect 4     PSet 2, part 2   : Due Sep. 15.
  Lecture 5     09/15     Geometry of topological vector spaces, Metrization     Lect 5   |   Typed Lect 5     PSet 3, part 1   : Due Sep. 22.
  Lecture 6     09/18     Seminorm, Frechet spaces     Lect 6   |   Typed Lect 6     PSet 3, part 2   : Due Sep. 22.   Quiz 1  
  Lecture 7     09/22     Convexity; Hilbert spaces     Lect 7     PSet 4, part 1   : Due Sep. 29.
  Lecture 8     09/25     Linear operators, Continuity v.s. boundedness, Finite dimensional spaces     Lect 8   |   Typed Lect 8     PSet 4, part 2   : Due Sep. 29.
  Lecture 9     09/29     The Banach-Steinhaus theorem, uniform boundedness principle     Lect 9   |   Typed Lect 9     PSet 5, part 1   : Due Oct. 13.   Quiz 2  
  Lecture 10     10/09     The open mapping theorem     Lect 10   |   Typed Lect 10     PSet 5, part 2   : Due Oct. 13.
      10/13     Examples; Exercises (By Yiran Cheng)       page 1   |   page 2   |   page 3       PSet 6, part 1   : Due Oct. 20.
  Lecture 11     10/16     The closed graph theorem, closable operators     Lect 11   |   Typed Lect 11     PSet 6, part 2   : Due Oct. 20.
  Lecture 12     10/20     The Hahn-Banach Theorem     Lect 12   |   Typed Lect 12     PSet 7, part 1   : Due Oct. 27.
  Lecture 13     10/23     The Geometric Hahn-Banach Theorem     Lect 13   |   Typed Lect 13     PSet 7, part 2   : Due Oct. 27.   Quiz 3  
  Lecture 14     10/27     The Weak Topology     Lect 14   |   Typed Lect 14     PSet 8, part 1   : Due Nov. 3.
  Lecture 15     11/3     The Weak * Topology     Lect 15   |   Typed Lect 15     PSet 9, part 1   : Due Nov. 10.
  Lecture 16     11/6     Compact convex sets     Lect 16   |   Typed Lect 16     PSet 9, part 2   : Due Nov. 10.
  Lecture 17     11/10     The dual and double dual spaces     Lect 17   |   Typed Lect 17     PSet 10, part 1   : Due Nov. 17.   Quiz 4  
  Lecture 18     11/13     Reflexive spaces     Lect 18   |   Typed Lect 18     PSet 10, part 2   : Due Nov. 17.
  Lecture 19     11/17     The adjoint operators     Lect 19   |   Typed Lect 19     PSet 11, part 1   : Due Nov. 24.
  Lecture 20     11/20     The closed range theorem     Lect 20   |   Typed Lect 20     PSet 11, part 2   : Due Nov. 24.
      11/24     Exercises (By Yiran Cheng)       Ex2    
  Lecture 21     11/27     The compact operators     Lect 21   |   Typed Lect 21     PSet 12, part 1   : Due Dec. 8.
      11/28     Midterm                    Solutions  
  Lecture 22     12/1     The Riesz-Fredholm Theory     Lect 22   |   Typed Lect 22     PSet 12, part 2   : Due Dec. 8.
  Lecture 23     12/4     The Fredholm Operators     Lect 23   |   Typed Lect 23     PSet 12, part 3   : Due Dec. 8.
  Lecture 24     12/8     The Spectrum     Lect 24   |   Typed Lect 24     PSet 13, part 1   : Due Dec. 15.
  Lecture 25     12/11     Bases of Hilbert spaces     Lect 25   |   Typed Lect 25     PSet 13, part 2   : Due Dec. 15.   Quiz 5  
  Lecture 26     12/15     Operators on Hilbert spaces     Lect 26   |   Typed Lect 26     PSet 14, part 1   : Due Dec. 22.
  Lecture 27     12/18     Spectrum of compact self-adjoint operators     Lect 27     PSet 14, part 2   : Due Dec. 22.
  Lecture 28     12/22     Functions of self-adjoint operators     Lect 28     PSet 15, part 1   : Due Dec. 29.
  Lecture 29     12/25     The Spectral Projections     Lect 29   |   Typed Lect 29     PSet 15, part 2   : Due Dec. 29.
  Lecture 30     12/29     Consequences of The Spectral Theorem     Lect 30     Quiz 6  
      1/8     Exercises (By Yiran Cheng)       Ex3    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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