Math 173 Homepage, Winter 2015-2016

Theory of Partial Differential Equations

Instructor: András Vasy

Office: 383M

Phone: 723-2226

E-mail: andras "at" math.stanford.edu

Office hours: M 2-3, W 10:30-11:30 and W 1:30-3, from week 2. During week 1, office hour on M 10:30-11:30 and Friday 2-3pm.

Office hours for finals week: Monday 9-10am and 2-3pm, Tuesday 11:30am-12:00noon, and Wednesday 1:30-3pm.

Course Assistant: Jun Gao

E-mail: Jun Gao jung2 "at" stanford.edu

Office: 380N

Office hours: T3-6pm, W5-6pm, F3:30-5:30pm.

The usual Wednesday office hour (5-6 pm) will be moved to 2:00 -3:00 pm, Wed, Feb 24.

Class location: MWF 9:30-10:20 pm, Room 380-380D.

Due to the possibility of displaced classes in the second half of the quarter, we plan on an extra lecture a week starting week 2 until week 5, at a time suitable for most students.

The extra lectures will be Fridays 11:30-12:20 or Thursdays 1:30-2:20. The first two are Friday, January 15 and Friday, January 22, 11:30-12:20, room 381U. The third is Thursday, January 28, 1:30-2:20 in Room 90-92Q. The fourth is Friday, February 5, 11:30-12:20, room 381U.

Textbook: due to the availability of lecture notes, the following are all `recommended'.

The running syllabus will change somewhat, corresponding to the extra lectures stated above, but should give an indication of the scope and speed of the course.

This course is similar to Math 220, but designed for undergraduate math majors.

It is the continuation of the honors analysis course 171, emphasizing rigorous (i.e. logically careful) proofs, in the spirit of 171.

The knowledge of measure theory, as presented in 172, is NOT a prerequisite of the class, though L^p spaces will be discussed as completions. The Fourier analysis part of 172 will be covered in this class.

Grading policy: The grade will be based on the weekly homework (25%), on the in-class (expected in the usual classroom, roughly at the usual class time, but with an extra half an hour, so perhaps at 9am) midterm exam (35%) and on the take home final exam (40%). The take home exam will be due at the end of the period of the regular exam for this time slot (11:30am on Tuesday, March 15), and will be available about a week before the deadline.

The homework will be due either in class or by 9am in the instructor's mailbox on the designated day, usually Thursdays. You are allowed to discuss the homework with others in the class, but you must write up your homework solution by yourself. Thus, you should understand the solution, and be able to reproduce it yourself. This ensures that, apart from satisfying a requirement for this class, you can solve the similar problems that are likely to arise on the exams.

The take home final is available!

The index of summation in Problem 5 in the top displayed formula on p.3 should be l, not k, and on the last line of p.2, where q is described, v should be in R^N (not R^n). This is fixed in the currently posted version. In problem 4, part (iv), a clarification has been added that the PDEs considered are on Euclidean space.

The midterm will be in class, on Wednesday, February 10th. It is a 75 minute exam starting at 9am: note the early start! Please come to class a few minutes early so that we can start on time.

The midterm covers the material through Chapter 7 of the lecture notes, i.e. all the material prior to the Fourier transform. The best practice is to make sure you know how to do the problems on Problem Sets 1-4.

A practice midterm is available, with solutions.

Lecture Notes

Below are the lecture notes. Note that these are restricted to Stanford students, and they should not be more broadly circulated.

Problem Sets