MATH5012 Real Analysis II, 2012-13

Announcement

• Course outline [Download file]
• From Feb 4 we will move to Rm 707, MMW Building, of 60 seats.
• In Lecture 2 we will first discuss Radon measures and their distribution functions on the real line. Then we move to a discussion on rectifiable curves and a proof of the isoperimetric inequality on the plane following [SS].
• In Lecture 4 we will first complete the proof of the isoperimetric inequality and then discuss a change of variables formula following chapter 7 of [R].
• In Lecture 5 we discuss the product measure and Fubini's theorem following [EG].
• In Lecture 6 we will discuss applications of Fubini's theorem. See pg 172, [R] and Rademacher's theorem in [EG].
• The midterm will be held on March 4. The coverage is lectures and exercises 1 to 6.
• We will meet at Rm 505, WMY (Wu Ho Man Yuen Building) starting from Feb 25. It is near to the train station.
• A set of lecture notes for Real I has been uploaded. Prof Chou will be most grateful if you spot and send him math or typo mistakes in these notes. [Download file]
• I will tell you your midterm score by emails. Non-CU students please let me have your email address. Contact me only if you are dubious about it.
• In Lecture 7 we will wrap up our discussion on Fubini's theorem.
• The notes now contain the newly added chapters 6,7 and 8. Please let me have your spotted mistakes. Thank you in advance. [Download file]
• In the rest of the lectures we will be concerned with Sobolev spaces.
• We will discuss minimization problems in the setting of Sobolev spaces in the last lecture.
• The final examination will be posted on next Monday and is due on April 29.
• A typed chapter nine on Sobolev spaces will be available by the end of May. Please check the web from time to time.
• The due date is April 29. You may discuss but should not copy from each other. You could send in the papers by emails.

General Information

Lecture Notes

• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4
• Lecture 5
• Lecture 6
• Lecture 7
• Lecture 8
• Lecture 9
• Lecture 10
• Lecture 11
• Lecture 12

Assignments

• Exercise 1
• Exercise 2
• Exercise 3
• Exercise 4
• Exercise 5
• Exercise 6
• Exercise 7
• Exercise 8
• Exercise 9
• Exercise 10
• Exercise 11

Quizzes and Exams

• Final Exam

Solutions

• Exercise 1 Solution
• Exercise 2 Solution
• Exercise 3 Solution
• Exercise 4 Solution
• Exercise 5 Solution
• Exercise 6 Solution
• Exercise 7 Solution
• Exercise 8 Solution
• Exercise 9 Solution
• Exercise 10 Solution
• Exercise 11 Solution