Heaviside step function

The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a <a href="/facts/Step_function/VnrEjo4B">step function</a> named after <a href="/facts/Oliver_Heaviside/ktYBpAt7">Oliver Heaviside</a>, the value of which is <a href="/facts/0_(number)/4NBRtKHc">zero</a> for negative arguments and <a href="/facts/1_(number)/m3wpSfMf">one</a> for positive arguments. Different conventions concerning the value H(0) are in use. It is an example of the general class of step functions, all of which can be represented as <a href="/facts/Linear_combination/CVjL6kuN">linear combinations</a> of translations of this one.
The function was originally developed in <a href="/facts/Operational_calculus/4rM3SuB8">operational calculus</a> for the solution of <a href="/facts/Differential_equation/9MGbE3Ca">differential equations</a>, where it represents a signal that switches on at a specified time and stays switched on indefinitely. Heaviside developed the operational calculus as a tool in the analysis of telegraphic communications and represented the function as 1.

Heaviside step function open-in-new

Heaviside step function