# 18.156: Differential Analysis, Spring 2012

## Richard Melrose

This is the home page for the course 18.156 at MIT for Spring 2012.Recent changes:

- Another typo fixed in the problems, there may be more.
- Two (significant) typos fixed in the problems thanks to Jonathan.
- Lecture 6: Elliptic operators on compact manifolds are Fredholm. The Laplacian. Constructing a local parametrix.
- Problem set 1 is up.
- Lecture 2: Dirac/Clifford. Constant coefficient Dirac operators, Clifford algebra, spin representation (stated only). Outline of local elliptic regularity for elliptic operators with smooth coefficients -- reduced to 3 Lemmas.
- Lecture 1: Coordinate invariant definitions of cotangent space and differential of a smooth map etc. Reminder of local elliptic regularity for constant coefficient operators.
- 10 February, 2012: Finally I am setting up the web-page. It may take a little while.
- Old changes

Basic facts:

- Lectures: TR 11-12:30 in 2-146.
- Office hour: W 10-11 is a possibility, or by arrangement.
- Email to me at rbm AT math.mit.edu will likely be answered!
- Problem sets
Cal

Namely, Feb - No exams or tests. Grades will be based on homework alone.
- Lecture notes

I will add here a brief description of what I actually said as we go along this year, plus suggestions as to what to read before/after lectures. - Syllabus May change a little with time but my best guess as to where I will go.