ABSTRACT
Green’s function methods are common occurrences in many areas of physics and engineering. Sometimes also referred to as an impulse response, they describe how a linear system behaves when responding to very particular inhomogeneities. In some sense, Green’s functions may be seen as more physical than partial differential equations when it comes to describing physical situations as they will tell us directly how the system behaves in response to inhomogeneities. This being said, there is a close connection between the two and the Green’s functions will be solutions to linear partial differential equations. 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. This may be accomplished by using either mirror image or series expansion techniques. Once the Green’s function is known, the solution to a problem with arbitrary inhomogeneities may be found by solving an integral.
