Dirac Delta Function

The Dirac delta function, also known as the unit impulse, is a generalized function on the real numbers whose value is zero everywhere except at zero, where it is infinite, with the property that its integral over the whole real line equals one. Because no ordinary function actually has this property, the delta function is modeled rigorously using limits or, more commonly in mathematics, measure theory and the theory of distributions developed by Laurent Schwartz. It is named after the physicist Paul Dirac and is applied routinely in physics and engineering to model point masses and concentrated loads; its name reflects its role as a continuous analogue of the discrete Kronecker delta.