Finite element

Looking pretty good. Feel free to add whatever seems appropriate - I didn't even mention the Galerkin method (though I gave them the idea), the Lax-Milgram theorem, etc. It might be appropriate to at least mention them.  Exercise 3 may be a little long since it requires them to use the pseudospectral method to compare with the second order finite element method.  And much more could be said when comparing numerical methods for PDEs ....  I think it would be good to bounce that section off Jared and/or Emily to see if they agree/disagree or have something to add.