ABSTRACT
Green's function methods are common occurrences in many areas of physics and engineering. Before applying Green's function methods to partial differential equations, it is worth looking at their application to ordinary differential equations. The Green's function for the two-dimensional wave equation has the same Fourier transform as its one- and three-dimensional counterparts. One advantage of using Green's function methods is that the Green's function of a system may often be found by referring to known fundamental solutions to the differential equations in question by altering the solution in order to account for the particular boundary conditions. In addition to solving linear problems, Green's function methods may also be employed to solve non-linear systems where the non-linearities may be regarded as small perturbations to an otherwise linear problem.
