Singularity functions are of class n where n runs from -2 through 0 to +2 for functions of engineering interest.

Singularity functions have no indefinite integral, but possess definite integrals running from -infinity to x.

They form a series such that this integral of a function of order n is the next one up in the series and the derivative is the next one down.

The singularity function of interest to EEs is called the dirac delta function or the (unit) impulse function in physics. It is of class n = -1

Its derivative is called a doublet or a couple, of class n=-2

Its integral is called the (Heaviside) step function, of class zero.