Lecture 7, Oct 14, 13:10-15:00

We introduced properties of the Green's function: 
the symmetry property, the Green's formula, ... based on the Stokes theorem
and the distributional interpretation of Green's function.

We leave the local property of G and Harnack's ineq to Prof Lin ChangShou's
class.

We showed the equivalence of
(1) existence of Green's function for general domain
(2) Poisson equation with zero Drichelet BC.
and showed how to superpose to get solutions of the Poisson equation
with general Dirichelet BC.

Next we move on to the heat equation, explaining well/ill posedness
of the forward/backard heat equation by looking at the Fourier modes.