The Heaviside function, also known as the unit step function or Heaviside step function and usually denoted as u_c , 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 x=c is usually of little importance, although it is sometimes defined as x=\tfrac12 .

It has the Laplace transform


for c>0 .

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