Green's Functions with Applications, 2nd Edition

Chapter 3

Green’s Functions for Ordinary Differential 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 differential equations. We begin with ordinary differential equations. In Sections 3.1 and 3.2 we show how Laplace transforms are used to find Green’s functions for initial-value problems. Figueiredo Camargo et al.1 call this type of Green’s function “one-sided.”

In the case of boundary-value problems, there are two techniques. In the operator method (Sections 3.3 and 3.5), solutions are constructed for regions to the right and ...