Ok, sharky, now you're ready for:
Consider a linear differential equation written in the general form
where L(x) is a linear, self-adjoint differential operator, u(x) is the unknown function, and f(x) is a known non-homogeneous term.
e.g. L(x) could be the Laplacian.
The solution can be written in integral form as:
Where G(x;x') is the Green's Function, which satisfies
(delta is the Dirac delta function, of course)
Returning to the example of L(x) being the laplacian operator, show that the Green's function for a 2-dimensional laplacian equation is:
G(x;x')= - ln(r) / 2 pi
Sorry, no part marks for work, answers due by 1pm Friday, no extensions!