ASL STEM

Definition

The Heaviside step function is a mathematical function denoted H(x), or sometimes theta(x) or u(x) (Abramowitz and Stegun 1972, p. 1020), and also known as the "unit step function." The term "Heaviside step function" and its symbol can represent either a piecewise constant function or a generalized function. When defined as a piecewise constant function, the Heaviside step function is given by H(x)={0 when x<0; 1/2 when x=0; 1 when x>0 . When defined as a generalized function, it can be defined as a function theta(x) such that integral[theta(x)phi^'(x)dx]=-phi(0) for phi^'(x) the derivative of a sufficiently smooth function phi(x) that decays sufficiently quickly (Kanwal 1998).

Source: http://mathworld.wolfram.com