UnitStep == 1 and
HeavisideTheta remains unevaluated. In addition,
D[UnitStep[x], x] is
x != 0 and
x == 0, whereas
D[HeavisideTheta[x],x] = DiracDelta[x].
It seems to me that
UnitStep is the idealization of a leading edge of a perfect pulse, whereas
HeavisideTheta[x] is like an ideal Fourier Transform of the ideal
UnitStep[x] function. Is this a good way to distinguish between the two, and are there any other significant programming or mathematical distinctions between the two functions?