represents the unit step function, equal to 0 for and 1 for .
represents the multidimensional unit step function which is 1 only if none of the are negative.
- Some transformations are done automatically when UnitStep appears in a product of terms.
- UnitStep provides a convenient way to represent piecewise continuous functions.
- UnitStep has attribute Orderless.
- For exact numeric quantities, UnitStep internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.
- UnitStep is 1.
Examplesopen allclose all
Basic Examples (4)
UnitStep is a piecewise function:
Numerical Evaluation (5)
Specific Values (4)
Evaluate for symbolic parameters:
Find a value of x for which the UnitStep[x]=1:
Function Properties (10)
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:
Differentiation and Integration (6)
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:
Integral Transforms (4)
Find the LaplaceTransform of UnitStep:
The convolution of UnitStep with itself:
Compute a step response for a continuous-time system:
Compute a step response for a discrete-time system:
Solve the time‐independent Schrödinger equation with piecewise analytic potential:
This gives the probability of the random variable being in the interval :
Here is the resulting probability plotted:
Construct the Walsh function:
Define a Bose–Einstein and a Maxwell–Boltzmann distribution function with UnitStep and Exp functions:
Find the representation of a mathematical expression with UnitStep in terms of FoxH:
Properties & Relations (4)
The derivative of UnitStep is a piecewise function:
The derivative of HeavisideTheta is a distribution:
Expand into UnitStep of linear factors:
Convert into Piecewise:
Wolfram Research (1999), UnitStep, Wolfram Language function, https://reference.wolfram.com/language/ref/UnitStep.html (updated 2007).
Wolfram Language. 1999. "UnitStep." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/UnitStep.html.
Wolfram Language. (1999). UnitStep. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UnitStep.html