國立清華大學數學系
實變數函數論一
Math 5130-00
(Fall
2006) Real Analysis (I)
General
Information
Hours and Days: T2T3T4 (i.e.
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: 劉珈銘 (R710, Ext:33024), 洪國智 (R732, Ext:33121)
Prerequisite:高等微積分一, 二
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 first semester we will focus on Lebesgue's
theory of measure and integration. Topics to be covered include:
1. Lebesgue measure and outer measure
2. Lebesgue measurable functions
3. Lebesgue integrals
4. Repeated integration
5. Differentiation
6. Lp spaces (if time permits)
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:
Exercises
from Chapter 3-7 in Wheeden-Zygmund’s book.
Quizzes (30%): There will be 5~7 quizzes based on homework assignments. Contact
your teaching assistants for details.
Two
midterm exam (40%): Each midterm exam worth 20% of the course grade. Dates of tests will be
determined during the first week of classes. (Solutions for Exam 1,
Exam 2.)
Final
Exam (30%): Time and date of final exam is
Click here
for the course syllabus