Distribution (mathematics) (generalized functions)
In mathematics, a distribution, also known as a generalized function, is a mathematical object that extends the concept of a Function (mathematics) to include Dirac delta function-like objects, which are not functions in the classical sense. Distributions are used to model phenomena that are not smooth, such as the Bend (physics) of a material or the behavior of a Neuromuscular control system. They are defined as Linear functionals on a space of Test functions, and are used to extend the notion of Derivative to non-differentiable functions. The theory of distributions was developed by Sergei Sobolev and Laurent Schwartz, and has applications in Partial differential equations, Signal processing, and Quantum mechanics.