| 1–2 | Review of Harmonic Functions and the Perspective We Take on Elliptic PDE | |
| 3 | Finding Other Second Derivatives from the Laplacian | |
| 4 | Korn's Inequality I | |
| 5 | Korn's Inequality II | Problem Set 1 due |
| 6 | Schauder's Inequality | |
| 7 | Using Functional Analysis to Solve Elliptic PDE | |
| 8 | Sobolev Inequality I | |
| 9 | Sobolev Inequality II | |
| 10–12 | De Giorgi-Nash-Moser Inequality | Problem Set 2 due |
| 13 | Nonlinear Elliptic PDE I | |
| 14 | Nonlinear Elliptic PDE II | |
| 15 | Barriers | |
| 16–17 | Minimal Graphs | Problem Set 3 due |
| 18–19 | Leray-Schauder Approach to Nonlinear PDE | |
| 20 | Gauss Circle Problem I | |
| 21 | Gauss Circle Problem II | |
| 22–24 | Fourier Analysis in PDE and Interpolation | |
| 25 | Applications of Interpolation | |
| 26 | Calderon-Zygmund Inequality I | |
| 27 | Calderon-Zygmund Inequality II | Problem Set 4 due |
| 28 | Littlewood-Paley Theory | |
| 29 | Strichartz Inequality I | |
| 30 | Strichartz Inequality II | |
| 31–34 | The Nonlinear Schrödinger Equation | Problem Sets 5 and 6 due |
