This page will be up until Terence Tao is able to return to UCLA. I will use it to supplement the official homepage, "Classpage (Tao)", which, as you can see, is still up!
CHANGES: The course enrollment limit has been raised to 30, so people who have not been able to enroll until now without PTE numbers should be able to enroll, and we now have a (slightly) larger room. Wednesday's class will be in MS5148 at the end of the corridor.
OFFICE HOURS
I will be holding office hours Mondays 2-3 and Tuesdays 11-12 until Professor Tao returns. These will be in my faculty office, MS5238.ASSIGNMENTS
As you can see from the official homepage, there will be assignments from Tao's book to be handed in this course. Here is the first one, due January 20:
Assignment 1: Exercise 1.2 OR Exercise 1.7 and Exercise 1.8. Exercise 1.2 is the Contraction Mapping Theorem which may be familiar to you, so you have the choice of doing that or Exercise 1.7 which proves a useful comparison theorem. Exercise 1.8 will be fun. OOPS! 1.8 will not be fun unless you make the assumption that t_1 and t_2 are SUCCESSIVE zeroes of u(t). In other words u(t) is not zero on the open interval (t_1,t_2).
Assignment 2: Exercise 1.15, Exercise 1.35 and the Bootstrap part of 1.22. In 1.15 (Levinson's Theorem) you can use the standard Euclidean norm for the Hilbert space norm, and in 1.35 you can use the standard symplectic form from Example 1.27. This assignment is due in class Friday, Jan. 27. NOTE: Professor Tao has been steadily updating the text of his book. Sometime in early January he added the problem 1.15 that I have assigned here. If problem 1.15 in your copy of the notes does not refer to "Levinson's Theorem", please see Class Page (Tao) and check the notes there. There is a small typo in the statement of 1.15: F(t) is just a vector-valued function. So "F in C(R -> end D)" should be "F in C(R -> D)". [ End D stands for the endomorphisms of D which is a classy way of saying linear maps of D into itself.]
Solutions to Assignment 2A little more on Exercise 2.4 which was not assigned but discussed in class last Friday
Assignment 3: Exercises 1.48 and 1.50. Both of these may have different numbers in your copies of the notes. 1.48 is called "Stability" and is related to Prop. 1.38. 1.50 derives the Duhamel formula for second order equations. This will be used later in the course. This assignment is due in class Monday, February 7.
Assignment 4: Exercise 2.23 and Exercise 2.24 from the notes. This assignment is due in class Monday, February 14.