Real Analysis, Math 156
Instructor Info: Larry
Guth, 2-278, email@example.com
Class times: MWF 3-4, 2-151
Office hours: Monday and Friday after class.
Course Description: In this course, we will
study elliptic PDE with variable coefficients building up
to the minimal surface equation. Then we will study
Fourier and harmonic analysis, emphasizing applications of
Fourier analysis. We will see some applications in
combinatorics/number theory, like the Gauss circle
problem, but mostly focus on applications in PDE, like the
Calderon-Zygmund inequality for the Laplacian, and the
Strichartz inequality for the wave equation and the
Schrodinger equation. In the last part of the
course, we will study these two dispersive PDE.
Along the way, we will work on the craft of proving
estimates. For a much more detailed description of
the class, you can click on the following link: Course
Notes and references:
In last year's class, Paul Gallagher, Cole Graham, Kevin Sackel, and Jane Wang typed up lecture notes for the class. A big thank you to them, and also to Spencer Hughes, who gave two guest lectures and typed up notes for them. I hope these notes can be a helpful reference. I'm planning to follow the same plan pretty closely.
Lectures 1 and 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9, Lectures 10 - 12, Lecture 13, Lecture 14, Lecture 15, Lectures 16-17.
Here are notes for the second half of the course, starting after spring break.
Lecture 20, Lecture 21, Lectures 22-24, Lecture 25, Lecture 26, Lecture 27, Lecture 28, Lecture 29, Lecture 30, Lectures 31-34.
If you want to brush up on Fourier analysis, the
undergraduate book Fourier Analysis by Stein and
Shakarchi is very readable, and it covers the background
in the subject that we will use. Here is a super-quick summary of some fundamental facts about Fourier analysis that you can review before we start the Fourier analysis unit. Fourier analysis quick review
Problem Set 1 (Due on
Wed, Feb 17).
Problem Set 2 (Due on
Wed, March 2). Also, here is the latex file of the pset: Problem Set 2 latex file.
Problem Set 3 (Due on
Wed, March 16).
Problem Set 4 (Due on
Fri, April 15).
Problem Set 5 (Due on
Mon, May 2).
Last problem set (Due on
Wed, May 11).
Further (optional) problems for study and review