This distribution can be considered the generalized derivative of the step function.
Substituting this mathematical object in for the inhomogeneous term in an integrodifferential equation yields the equation satisfied by the associated Green's function. This object is the fundamental example of the class of abstract sequentially continuous linear functionals on non-metric vector spaces of C-infinity-zero functions; such objects are known as singular distributions. Operation of convolution with a sequence approximating this functional converges in distribution to the identity operation. Therefore, the convolution of this object with any function f yield f of zero, a fact known as the sifting property. This distribution can be considered the generalized derivative of the step function. For 10 points, name this mathematical object that can be understood as a spike of unit area, zero width, and infinite height.
Substituting this mathematical object in for the inhomogeneous term in an integrodifferential equation yields the equation satisfied by the associated Green's function.
Dirac delta function [prompt on delta function]