Math 173 Homepage, Winter 2015-2016
Theory of Partial Differential Equations
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
Course Assistant: Jun Gao
E-mail: Jun Gao jung2 "at" stanford.edu
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
Textbook: due to the availability of lecture notes, the following are
Strauss' `Partial Differential Equations: An introduction' covers most
topics, but the course
is at a higher level, especially regarding first order PDE's, which is
the first major topic covered, as well as distributions and the Fourier
Evans' `Partial Differential Equations' is
a more advanced text, and it covers course topics not dealt with in Strauss'
Pinchover and Rubinstein's `An introduction to partial differential
equations'. This is a fairly good match for the level of difficulty of
the course, though does not necessarily cover the same topics/the same way.
All of these, as well as John's `Partial Differential Equations'
will be on reserve at the Math library.
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
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 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
Below are the lecture notes. Note that these are restricted to
Stanford students, and they should not be more broadly circulated.
- Problem Set 1, due Thursday, January
14, 9am. Solutions.
- Problem Set 2, due Thursday, January
Postponed to Friday, January 22, 10am (in class).Solutions.
- Problem Set 3, due Thursday, January
28, 2pm. Solutions.
- Problem Set 4, due Monday, February
8, 10am. Solutions.
- Problem Set 5, due Friday, February
Problem 6 delayed until Problem Set 6!Solutions.
- Problem Set 6, due Friday, February
The constant in Problem 6, part ii, iv, in front of
the exponential should be pi to the power -n/4; this is updated in
the currently posted version.Solutions.
- Problem Set 7, due Friday, February
Due to instructor unavailability, the problem set is
postponed to Monday, February 29, 10am. Problem Set 8 will still be due on
Friday, March 4. Solutions.
- Problem Set 8, due Friday, March 4, 10am. Solutions.
- Problem Set 9, due Wednesday, March 9, 10am. Solutions.