Heaviside Step Function

This function was developed by a brilliantand quirky Englishman named Oliver Heaviside.

The function acts as a mathematical 'on-off' switch.The argument of the function, denoted Φ(x), is the point at which the switch turns on. When x<0, Φ=0.When x>0, Φ=1. Also, Φ(0)=1.

The Heaviside step function is a standard functionin Mathcad

Oliver Heaviside (Wikipedia)

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Φ x( )

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There are a number of functions that approximate Φ(x). For example:

H k x,( )1

1 e k− x⋅+

:= <= k determines how quickly the function switches

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H 1 x,( )

H 2 x,( )

H 5 x,( )

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