國立清華大學數學系
實變數函數論二
Math 5131-00 (Spring 2010) Real Analysis II
Instructor:
Hours and days: F5F6F7
Classroom: 綜三 631
Office: 綜三 609
Office Hours: R7R8, or by appointments
Phone Number: (03) 5715131 Ext: 33067
Email: kchen@math.nthu.edu.tw
Teaching Assistant:陳志豪 (R644)
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.
References
H.L.Royden: Real Analysis, Macmillian, 1988.
E. M. Stein & R. Shakarchi: Real Analysis,
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. Lebesgue differentiation theorem
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 9~12 in Wheeden-Zygmund’s book. Some of them will be
collected and graded. Contact your teaching assistant for details.
Two midterm exam (40%): Each midterm exam worth 20% of the course grade. Dates
of tests are Friday, April 9 and Friday, May 14.
Final Exam (30%): Time and date of final exam are 13:00-16:00, June 18
(Friday).