Heaviside step function: Difference between revisions

Revision as of 11:40, 20 February 2024

Revision as of 12:59, 30 March 2024

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| fields_of_application = Operational calculus

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The '''Heaviside step function''', or the '''unit step function''', usually denoted by {{mvar|H}} or {{mvar|θ}} (but sometimes {{mvar|u}}, {{math|'''1'''}} or {{math|{{not a typo|𝟙}}}}), is a [[step function]] named after [[Oliver Heaviside]], the value of which is [[0 (number)|zero]] for negative arguments and [[1 (number)|one]] for positivenonnegative arguments.<ref name="Zhang Zhou 2021 pp. 9–46">{{cite book | last=Zhang | first=Weihong | last2=Zhou | first2=Ying | title=The Feature-Driven Method for Structural Optimization | chapter=Level-set functions and parametric functions | publisher=Elsevier | year=2021 | doi=10.1016/b978-0-12-821330-8.00002-x | pages=9–46 | quote=Heaviside function, also called the Heaviside step function, is a discontinuous function. As illustrated in Fig. 2.13, it values zero for negative input and one for nonnegative input.}}</ref> It is an example of the general class of step functions, all of which can be represented as [[Linear combination|linear combinations]] of translations of this one.

The function was originally developed in [[operational calculus]] for the solution of [[differential equation]]s, where it represents a signal that switches on at a specified time and stays switched on indefinitely. [[Oliver Heaviside]], who developed the operational calculus as a tool in the analysis of telegraphic communications, represented the function as {{math|'''1'''}}.