ABSTRACT
D Dirac Delta Function The Dirac delta function (sometimes called the unit impulse function) plays a central role in the method of Green’s functions. The Dirac delta function δ(x) is defined to be zero when x = 0, and infinite at x = 0 in such a way that the area under the function is unity. A concise definition is the following: given nonzero numbers η1 > 0 and η2 > 0,
δ(x) = 0 if x = 0; ∫ η2 −η1
δ(x) dx = 1 (D.1)
This is a “weak” definition of δ(x), since the limits of integration are never allowed to be precisely zero. This definition is sufficient for work with Green’s functions. See Barton (1989, p. 11) for a discussion of “weak” and “strong” definitions.
