Ramp

Ramp[x]

gives x if x0 and 0 otherwise.

Details

  • Ramp automatically threads over lists.

Examples

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Basic Examples  (3)

Evaluate numerically:

Plot over a subset of the reals:

Ramp is a piecewise function:

Scope  (24)

Numerical Evaluation  (4)

Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate efficiently at high precision:

Ramp threads over lists:

Specific Values  (5)

Values of Ramp at fixed points:

Value at zero:

Values at infinity:

Evaluate symbolically:

Find a value of x for which Ramp[x]1:

Visualization  (4)

Plot the Ramp function:

Visualize shifted Ramp functions:

Visualize the composition of Ramp with a periodic function:

Plot Ramp in three dimensions:

Function Properties  (3)

Ramp is defined for all real numbers:

It is restricted to real inputs:

Function range of Ramp:

Ramp is equivalent to the average of a number with its RealAbs:

Differentiation and Integration  (4)

First derivative with respect to x:

Except for the singular point , this derivative is UnitStep:

Second derivative with respect to x:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Definite integral:

Integral Transforms  (4)

FourierTransform of Ramp:

FourierSeries:

LaplaceTransform of Ramp:

The convolution of UnitStep with itself is equal to Ramp:

The convolution of Ramp and UnitStep gives a quadratic on the non-negative reals:

The convolution of Ramp with itself gives a cubic on the non-negative reals:

Applications  (2)

Integrate a piecewise function involving Ramp symbolically and numerically:

Solve a differential equation involving Ramp:

Plot the solution for different values of a:

Properties & Relations  (1)

Ramp is related to UnitStep:

Introduced in 2016
 (11.0)