The **Heaviside function**, also known as the **unit step function** or **Heaviside step function** and usually denoted as , is a discontinuous function that

The Heaviside function can be defined as the integral of the Dirac delta function.

The Heaviside function is often used in differential equations to model non-continuous events such as force in a driven harmonic oscillator or voltage in a circuit. If the Dirac delta function represents force being applied on an object, the Heaviside function will represent its momentum.

The value at is usually of little importance, although it is sometimes defined as .

It has the Laplace transform

for .