- Sifting property. Given function continuous at
,

When integrated, the product of any (well-behaved) function and the Dirac delta yields the function evaluated where the Dirac delta is singular. The sifting property also applies if the arguments are exchanged: . - Integral.

where is the Heaviside unit step function defined as

- Units. Since the definition of the Dirac delta requires that the
product is dimensionless, the units of the Dirac delta are
the inverse of those of the argument . That is, has units , and has units .
- Definition for radial, 2-D, and 3-D geometries. For two- and three-
dimensional problems with vector coordinate
,
the Dirac delta function is defined:

where is differential volume. The units of are given by [], and three important cases are the listed below.- 1-D radial cylindrical coordinates: , and units of
are [meters].
- 1-D radial spherical coordinates:
and units of
are [meters].
- 2-D Cartesian coordinates: dv = dx dy, and units of are [meters].

- 1-D radial cylindrical coordinates: , and units of
are [meters].