Evaluate numerically:

UnitStep always returns an exact result:

Evaluate efficiently at high precision:

UnitStep can deal with real‐valued intervals:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix UnitStep function using MatrixFunction :

Compute average-case statistical intervals using Around :

Value at zero:

Value at infinity:

Evaluate for symbolic parameters:

Find a value of x for which the UnitStep [x]=1:

Plot the UnitStep function:

Visualize shifted UnitStep functions:

Visualize the composition of UnitStep with a periodic function:

Plot UnitStep in three dimensions:

Function domain of UnitStep :

It is restricted to real inputs:

Function range of UnitStep :

UnitStep has a jump discontinuity at the point :

UnitStep is not an analytic function:

It has both singularities and discontinuities:

UnitStep is nondecreasing:

UnitStep is not injective:

UnitStep is not surjective:

UnitStep is non-negative:

UnitStep is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to x:

All higher-order derivatives the same:

First derivative with respect to z:

Compute the indefinite integral using Integrate :

Verify the anti-derivative away from the singular point:

Definite integral:

Integral over an infinite domain:

FourierTransform of UnitStep :

FourierSeries :

Find the LaplaceTransform of UnitStep :

The convolution of UnitStep with itself: