Why 0.5 in value of heaviside/unitstep?

1. What is the value of the Heaviside function at 0?
2. What is the value of unit step function at 0?
3. Why do we use Heaviside function?

What is the value of the Heaviside function at 0?

Mathematical Preliminaries

The Heaviside step function H(x), also called the unit step function, is a discontinuous function, whose value is zero for negative arguments x < 0 and one for positive arguments x > 0, as illustrated in Fig. 2.2.

What is the value of unit step function at 0?

We do not define u(t) at t = 0. Rather, at t = 0 we think of it as in transition between 0 and 1. It is called the unit step function because it takes a unit step at t = 0. It is sometimes called the Heaviside function.

Why do we use Heaviside function?

The heaviside function is a very simple piecewise function, defined on an infinite interval . It is denoted as H(t) and historically the function will only use the independent variable "t", because it is used to model physical systems in real time.