Heaviside step function: Difference between revisions

Revision as of 23:56, 18 August 2022

Revision as of 16:32, 11 November 2022

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The Heaviside function may be defined as:

* a [[piecewise function]]: <math display="block">H(x) := \begin{cases} 1, & x > 0 \\ 0, & x \le 0 \end{cases}</math>

* anusing the [[indicatorIverson functionbracket]]: notation" <math display="block">H(x) := \mathbf{1}_{[x > 0}]</math>

* an [[indicator function]]: <math display="block">H(x) := \mathbf{1}_{x > 0}=\mathbf 1_{\mathbb R_+}(x)</math>

* the derivative of the [[ramp function]]: <math display="block">H(x) := \frac{d}{dx} \max \{ x, 0 \}\quad \mbox{for } x \ne 0</math>