21272  Introduction to PDEs
Overview
The aim of the course is to give a broad overview of the most important first and second order linear PDEs (namely, transport equation, Laplace equation, heat equation
and wave equation) as well as of some nonlinear ones. In particular, Fourier series and Fourier transform will be introduced and applied to study some linear PDEs.
Time permitting, some topics from first order nonlinear PDEs will be covered.
Material
Notes
The following are the notes I used for the classes. Please take into consideration that errors may be present! Some are handwritten, some are typed in Latex.



The transport equation (pdf  730kb)

Diffusion equation  derivation and derivation of the heat kernel (pdf  404kb)

Diffusion equation in the whole space (pdf  308kb)

Diffusion equation  separation of variables (pdf  137kb)

Wave equation  fast and loose derivation (pdf  145kb)

Wave equation  rigorous derivation (pdf  409kb)

Wave equation  d'Alembert formula (pdf  106kb)

Wave equation  separation of variables (pdf  119kb)

Energy and uniqueness (pdf  101kb)

Fourier series  computation of coefficients (pdf  83kb)

Fourier series  review (pdf  187kb)

Fourier series  properties (pdf  109kb)

Fourier series  solution of the heat equation (pdf  123kb)

Fourier series  solution of the wave equation (pdf  84b)

Forcing term in the wave equation in bounded domains (pdf  100kb)

The divergence theorem (pdf  600kb)

Laplace and Poisson equation in bouthe whole space (pdf  134kb)

The Laplacian in polar and spherical coordinates (pdf  119kb)

Laplace equation in bounded domains (pdf  136kb)

Poisson formula for balls (pdf  158kb)


