Lecture Notes

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)