| SES # | TOPICS | KEY DATES |
|---|---|---|
| L1 | Introduction to PDEs | |
| L2 | Introduction to the heat equation | |
| L3 | The heat equation: Uniqueness | Problem Set 1 due |
| L4 | The heat equation: Weak maximum principle and introduction to the fundamental solution | |
| L5 | The heat equation: Fundamental solution and the global Cauchy problem | Problem Set 2 due |
| L6 | Laplace's and Poisson's equations | |
| L7 | Poisson's equation: Fundamental solution | Problem Set 3 due |
| L8 | Poisson's equation: Green functions | |
| L9 | Poisson's equation: Poisson's formula, Harnack's inequality, and Liouville's theorem | Problem Set 4 due |
| L10 | Introduction to the wave equation | Problem Set 5 due |
| L11 | The wave equation: The method of spherical means | |
| L12 | The wave equation: Kirchhoff's formula and Minkowskian geometry | Problem Set 6 due |
| L13 | The wave equation: Geometric energy estimates | |
| E1 | Midterm Exam | |
| L14 | The wave equation: Geometric energy estimates (cont.) | |
| L15 | Classification of second order equations | Problem Set 7 due |
| L16 | Introduction to the Fourier transform | |
| L17 | Introduction to the Fourier transform (cont.) | Problem Set 8 due |
| L18 | Fourier inversion and Plancherel's theorem | |
| L19 | Introduction to Schrödinger's equation | Problem Set 9 due |
| L20 | Introduction to Schrödinger's equation (cont.) | |
| L21 | Introduction to Lagrangian field theories | Optional (Bonus) Problem due |
| L22 | Introduction to Lagrangian field theories (cont.) | Problem Set 10 due |
| L23 | Introduction to Lagrangian field theories (cont.) | |
| L24 | Transport equations and Burger's equation | Problem Set 11 due |
| E2 | Final Exam |