Introduction to Partial Differential Equations

Calendar

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