18.152  Intro: Partial Diff Equations

Have a great summer!

If you email me on Thursday, I will reply with your grade. You guys were a great group and I really enjoyed teaching the class. I hope that you all have a great summer!

WPM

Announced on 20 May 2014  3:00  p.m. by William Minicozzi

Final exam - announcement

Monday's final will have 8 questions covering:

1. One-dimensional wave equation (2 problems).
2. Harmonic functions, maximum principle and energy (2 problems).
3. Scaling/integration by parts/nonlinear pde (e.g., Pohozaev) (1 problem).
4. Drift operator and related questions (1 problem).
5. Discrete pde - energy, discrete Laplacian (1 problem).
6. The heat equation - maximum principle/heat kernel/energy (1 problem).

This is covered in the online lecture notes, except for the wave equation questions. Use either course notes, the text book or Evans' book for this.

See you tomorrow.

Announced on 18 May 2014  8:03  a.m. by William Minicozzi

Homework 5 is posted.

Announced on 14 April 2014  4:45  p.m. by William Minicozzi

Midterm next week

We have a midterm in class on 3/20. Topics include:
1. All material on harmonic functions (both from Chapter 3 in the text and from lectures).
2. The Pohozaev identity and its consequences (including for L^2 eigenfunctions).
3. The drift Laplacian.
4. The heat equation from this week's lectures and the first four sections of chapter 2 in the text.

Announced on 13 March 2014  1:34  p.m. by William Minicozzi

3.18(a) on the homework is wrong

For 3.18(a) from the text: This problem is wrong. Explain why (i.e., give a counterexample).

Announced on 06 March 2014  6:56  a.m. by William Minicozzi