| L1 | Introduction to PDEs | (PDF) |
| L2 | Introduction to the heat equation | (PDF) |
| L3 | The heat equation: Uniqueness | (PDF) |
| L4 | The heat equation: Weak maximum principle and introduction to the fundamental solution | (PDF) |
| L5 | The heat equation: Fundamental solution and the global Cauchy problem | (PDF) |
| L6 | Laplace's and Poisson's equations | (PDF) |
| L7 | Poisson's equation: Fundamental solution | (PDF) |
| L8 | Poisson's equation: Green functions | (PDF) |
| L9 | Poisson's equation: Poisson's formula, Harnack's inequality, and Liouville's theorem | (PDF) |
| L10 | Introduction to the wave equation | (PDF) |
| L11 | The wave equation: The method of spherical means | (PDF) |
| L12 | The wave equation: Kirchhoff's formula and Minkowskian geometry | (PDF) |
| L13–L14 | The wave equation: Geometric energy estimates | (PDF) |
| L15 | Classification of second order equations | (PDF) |
| L16–L18 | Introduction to the Fourier transform; Fourier inversion and Plancherel's theorem | (PDF) |
| L19–L20 | Introduction to Schrödinger's equation | (PDF) |
| L21-L23 | Introduction to Lagrangian field theories | (PDF) |
| L24 | Transport equations and Burger's equation | (PDF) |
