SCHEDULE
Note: The schedule is subject to change. Check back for changes and updates
| Date | Topic | ||
|---|---|---|---|
| 2/12 | Problem set 1 due | ||
| 2/17 | No class; Presidents' Day | ||
| 2/18 | Monday schedule of classes to be held. Section 2.1.5, 2.2 | ||
| 2/19 | Barrier, Li-Yau Harnack inequality, Backward uniqueness | ||
| 2/24 | Section 3.1, 3.2, Enery minimizer and gradient flow | ||
| 2/26 | Problem set 2 due, Section 3.3.2, 3.3.3 | ||
| 3/2 | Section 3.3.4, Separation of variables | ||
| 3/4 | Section 3.6-7 | ||
| 3/9 | Section 3.7, 3.3.5-7 | ||
| 3/11 | Section 3.5, Proof of Theorem 3.5. | ||
| 3/16-27 | Spring break | ||
| 3/30 | Q&A session 1 - Higher order estimates for solutions to Poisson equation | ||
| 4/1 | Problem set 3 due, Q&A session 2 - Schauder estimates I | ||
| 4/6 | Q&A session 3 - Schauder estimates II | ||
| 4/8 | Midterm assignment due, Q&A session 4 - Banach space | ||
| 4/13 | Q&A session 5 - Introduction to the wave equation | ||
| 4/15 | Problem set 4 due, Q&A session 6 - 1D Cauchy problem | ||
| 4/20 | No class; Patriots Day | ||
| 4/22 | Q&A session 7 - Cauchy problem in higher dimensions | ||
| 4/27 | Q&A session 8 - Energy estimates | ||
| 4/29 | Problem set 5 due, Q&A session 9 - Eigenfunctions and Eigenvalues | ||
| 5/4 | Q&A session 10 - Hilbert space and Existence of eigenfunctions | ||
| 5/6 | Problem set 6 due, Q&A session 11 - Weak convergence | ||
| 5/11 | Q&A session 12 - Eigenfunctions span L^2 space | ||
| 5/12 | Final assignment due |
