Partial Differential Equations Math 222A

Instructor: Maciej Zworski

Lectures: TuTh 1230-2PM, 6 EVANS

Course Control Number: 54424

Office: 801

Office Hours: Tu 2:15-4 PM

Prerequisites: 202A or equivalent

Required Text: L.C. Evans, Partial Differential Equations; L. Hörmander, The Analysis of Linear Partial Differential Operators, vol.I.

Syllabus: The course, and its sequel Math 222B, will provide a comprehensive introduction to the theory of partial differential equations. Math 222A: transport, Laplace's, wave, and heat equations; nonlinear first order scalar equations, Hamilton-Jacobi equations, viscosity solutions (Evans); theory of distributions, Fourier transform, linear equations with constant coefficients (Hörmander). Math 222B: Sobolev spaces, 2nd order elliptic equations, spectral theory, calculus of variations (Evans) + additional topics (e.g. Schauder estimates, Moser's paper on the Nash-DeGiorgi theorem; Calderón's paper on the linearized inverse conductivity problem).

Course Webpage:

Grading: The grade will be based on weekly homework.

Homework: Homework will be assigned every week and due the following week.