國立清華大學數學系

實變數函數論二
Math 5131-00 (Spring 2007) Real Analysis (II)

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General Information

Hours and Days: T2T3T4 (i.e. 9:00 ~ 12:00 T)
Classroom: 綜三 723
Instructor: 陳 國 璋
Office: 綜三 609

Office Hours: T5T6W4, or by appointments
Phone Number: (03) 5715131 Ext: 33067
Email: kchen@math.nthu.edu.tw

Teaching Assistants:洪國智 (R732, Ext:33121)

Prerequisite:實變函數論一
Textbook:

R.L.Wheeden and A.Zygmund: Measure and Integral - An introduction to Real Analysis, Marcel Dekker, 1977.

Reference:

H.L.Royden: Real Analysis, Macmillian, 1988.

W.Rudin: Real and Complex Analysis, McGraw-Hill, 1987.

Course Description: This course is an introduction to the theory of measure and integration.
In the second semester we will introduce abstract theory of measure and integration, and some elements of harmonic analysis. Topics to be covered include:
1. L^p spaces
2. Maximal functions
3. Abstract integration
4. Measure and outer measure
5. Fourier series

Attendance: Students are expected to attend every scheduled class. It is the student's responsibility to keep informed of any announcements, syllabus adjustments or policy changes made during scheduled classes.

Grading

Homework/Quizzes (30%): Exercises from Chapter 8-12 in Wheeden-Zygmund’s book. Some of them will be collected and graded. Contact your teaching assistants for details.

Two midterm exam (40%): Each midterm exam worth 20% of the course grade. Dates of tests are Wednesday, April 11 and Wednesday, May 16. (Solutions for Exam 1, Exam 2)

Final Exam (30%): Time and date of final exam are 9:00-12:00, June 26 (Tuesday).

Click here for the course syllabus