| Week | Date (Monday) | Monday | Wednesday | Friday |
| 0 | 9/21 | First order linear PDE | ||
| 1 | 9/28 | Basic Laplace Equation |
Average Value Property, Dirichlet Principle |
Direct Methods in the Calculus of Variations |
| 2 | 10/5 | Continuation of Direct Methods | Interior Regularity for Laplace |
Schauder Estimates I: Interior Regularity |
| 3 | 10/12 | Schauder Estimates II: Continuation of Interior Regularity |
Schauder Estimates III: Boundary Regularity |
Schauder Estimates IV: Continuation of Boundary Regularity |
| 4 | 10/19 |
Schauder Estimates V: General Elliptic Equations |
Schauder Estimates V: General Elliptic Equations |
Maximum Principle, Continuity, & Applications |
| 5 | 10/26 | Some Non-Linear Problems | Difference quotients and higher regularity | Continuation of difference quotients and higher regularity |
| 6 | 11/2 | Heat Flow on R^n, Heat Kernel |
Heat Flow on domains, Eigenfunction expansions |
Existence for general linear heat flows |
| 7 | 11/9 | Parabolic Schauder Theory | Holiday | Parabolic Schauder Theory |
| 8 | 11/16 | Wave | Wave | Wave |
| 9 | 11/23 | Wave | Wave | Holiday |
| 10 | 11/30 | Wave | Wave | Wave |