Mathematica's symbolic character allows it to handle generalized functions or "distributions" as a direct extension of classical mathematical functions, and to represent integrals and integral transforms that cannot be expressed in terms of continuous functions.
DiracDelta — one-dimensional or multidimensional delta function
HeavisideTheta — Heaviside step function, for and for
Convolve — convolve generalized functions
FunctionExpand — expand out generalized functions