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MATHEMATICA GUIDE
Generalized Functions
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.
Reference
DiracDelta — one-dimensional or multidimensional delta function
HeavisideTheta — Heaviside step function, 
for 
and 
for 
DiracComb ▪ HeavisidePi ▪ HeavisideLambda
Integrate, D — integrals and derivatives of generalized functions
LaplaceTransform, FourierTransform — integral transforms
Convolve — convolve generalized functions
FunctionExpand — expand out generalized functions
