ABSTRACT
Chapter 2
Green's Functions
for Ordinary Dierential Equations
Having given a general overview of Green's functions, we provide
over the next four chapters the Green's functions for a wide class of
ordinary and partial dierential equations. We begin with ordinary dif-
ferential equations. In xx2.1 and 2.2 we show how Laplace transforms
are used to nd Green's functions for initial-value problems. In the case
of boundary-value problems, there are two techniques. In the operator
method (xx2.3 and 2.5), solutions are constructed for regions to the right
and left of the point of excitation and then pieced together to give the
complete Green's function. This is quite dierent from modal expan-
sions presented in x2.4, which express the Green's function in terms of
a superposition of eigenfunctions that are valid over the entire domain.
We conclude the chapter by introducing the property of reciprocity: the
response at x due to a delta function at equals the response at due
to a delta function at x.
