Short Course Description
Introduction
First Order PDEs
The wave equation in one space dimension: initial-value problem and initial-boundary-value problems, characteristics, Fourier expansions, waves and reflection, energy and uniqueness, stability and well-posedness
Classification of PDEs and canonical forms
Solution of PDEs by Fourier series and integrals: expansions in one and several dimensions, convergence, well-posedness and ill-posedness, application to the Laplace, Poisson, heat, and wave equations in various domains
Maximum principle and energy method: estimates, uniqueness
Green's functions
Full syllabus will be available to registered students only
