Ok, sharky, now you're ready for:

Consider a linear differential equation written in the general form

L(x)u(x)=f(x)

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:

http://www.boulder.nist.gov/div853/greenfn/pictures/Image15.gif

Where G(x;x') is the Green's Function, which satisfies

L(x)G(x;x')=delta(x-x')

(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!