实分析（2018春季学期）


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 (05/14) List of Projects uploaded.

o (06/14) Recitation 3 uploaded.

o (06/14) Lecture 28 uploaded.

o (06/14) 答疑： 06/21， 19:00-21:00 at 5403.

课程信息

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

o 上课时间：   星期一上午 9:45am – 12:10pm; 星期四上午 9:45am – 11:20am　

o 上课地点：   五教 5403

o 办公室：   管研楼1601

o 助教：   Yufeng Zhang (alienf at mail dot ustc dot edu dot cn)，Mengxin Yu (ymx9856 at mail dot ustc dot edu dot cn)

o 答疑时间：   15:55-17:30， Sundays

o 答疑地点：   5403

o 小论文： List of Projects

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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 作业在每周一课前交。

序号 日期 内容 讲义 作业
  Lecture 1     02/26     Introduction: What is real analysis?     Lect 1     PSet 1, part 1   : Due March 5.
  Lecture 2     03/01     Elementary measure， Jordan measure     Lect 2     PSet 1, part 2   : Due March 5.
  Lecture 3     03/05     Lebesgue outer measure     Lect 3     PSet 2, part 1   : Due March 12.
  Lecture 4     03/08     Lebesgue measure     Lect 4     PSet 2, part 2   : Due March 12.
  Lecture 5     03/12     Lebesgue measure (continued)     Lect 5     PSet 3, part 1   : Due March 19.
  Lecture 6     03/15     Measurable functions     Lect 6     PSet 3, part 2   : Due March 19.
  Lecture 7     03/19     Convergences of measurable functions     Lect 7     PSet 4, part 1   : Due March 26.
  Lecture 8     03/23     Approximation by simple and/or continuous functions     Lect 8     PSet 4, part 2   : Due March 26.
  Lecture 9     03/26     Lebesgue integrals of nonnegative measurable functions     Lect 9     PSet 5, part 1   : Due April 02.
  Lecture 10     03/29     Convergence of Lebesgue integrals：nonnegative measurable functions     Lect 10     PSet 5, part 2   : Due April 02.
      04/02     习题课     Recitation 1    
  Lecture 11     04/09     Lebesgue integrals of general measurable functions     Lect 11     PSet 6, part 1   : Due April 16.
  Lecture 12     04/12     Convergence of Lebesgue integrals：absolutely integrable functions     Lect 12     PSet 6, part 2   : Due April 16.
  Lecture 13     04/16     Lebesgue integrals v.s. Riemann integrals, Fubini's theorem     Lect 13     PSet 7, part 1   : Due April 23.
  Lecture 14     04/19     More on Lebesgue integrals: Tonelli's theorem, Convolution     Lect 14     PSet 7, part 2   : Due April 23.
  Lecture 15     04/23     Abstract measures     Lect 15     PSet 8, part 1   : Due May 3.
  Lecture 16     04/26     Integrations on abstract measure spaces     Lect 16     PSet 8, part 2   : Due May 3.
  Lecture 17     04/28     From outer measures to measures   Lect 17     PSet 9, part 1   : Due May 7.
      04/28     MIDTERM: Cover Lecture 1- Lecture 14  
  Lecture 18     05/03     Metric v.s. measure     Lect 18     PSet 9, part 2   : Due May 7.
  Lecture 19     05/07     The Riesz representation theorem     Lect 19     PSet 10, part 1   : Due May 14.
  Lecture 20     05/10     Lp spaces     Lect 20     PSet 10, part 2   : Due May 14.
  Lecture 21     05/14     Lp spaces as metric spaces     Lect 21     PSet 11, part 1   : Due May 21.
  Lecture 22     05/17     L2 spaces as inner product spaces     Lect 22     PSet 11, part 2   : Due May 21.
      05/21     习题课     Recitation 2    
  Lecture 23     05/24     Riesz representation theorem for Lp spaces     Lect 23     PSet 12, part 1   : Due May 28.
  Lecture 24     05/28     Signed measure, the Lebesgue-Radon-Nikodym theorem     Lect 24     PSet 13, part 1   : Due June 04.
  Lecture 25     05/31     The Lebesgue differentiation theorem     Lect 25     PSet 13, part 2   : Due June 04.
  Lecture 26     06/04     The fundamental theorem of calculus     Lect 26     PSet 14, part 1   : Due June 11.
  Lecture 27     06/07     The Rademacher differentiation theorem     Lect 27     PSet 14, part 2   : Due June 11.
      06/11     习题课     Recitation 3    
  Lecture 28     06/14     Review     Lect 28    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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