Discussed Poisson's equation, Laplace's equation (also wave and diffusion equations)
Solved very simple example of Laplace's equation, potential and electric field between two large capacitor plates.
Uniqueness theorem - there is only one solution to Poisson's equation with given boundary conditions (i.e. values of the function on a closed boundary surface)
The proof involves assuming there are two different solutions, forming their difference, X, noting that X is 0 on the boundary, and satisfies Laplace's equation throughout the volume. Then one constructs a very inobvious function Div(X grad X), and you apply the divergence theorem over the whole volume inside the boundary.
Reminder of the handy formulas at the very end of Boas Ch. 6 (after the problems), one of which we used to expand the scary-looking divergence above
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