Introduction to Partial Differential Equations

Lecture Notes

SES #	TOPICS	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)