FANDOM


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

u_c(x)=\begin{cases}0&x<c\\1&x>c\end{cases}

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

u_c(t)=\int\limits_{-\infty}^t\delta(s-c)ds

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

\mathcal{L}\{u_c(t)\}=\frac{e^{-cs}}{s}

for c>0 .

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.