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Heaviside step function
Sign in to saveAlso known as unit step function, Heaviside function
discontinuous function whose value is zero for negative numbers and one for positive numbers
Key facts
- General definition
- H ( x ) := { 1 , x ≥ 0 0 , x < 0 {\displaystyle H(x):={\begin{cases}1,&x\geq 0\\0,&x<0\end{cases}}}
- Fields of application
- Operational calculus
via Wikipedia infobox
Wikidata facts
- Instance of
- step function
- Named after
- Oliver Heaviside
Show 4 more facts
- Commons category
- Heaviside function
- definition domain
- set of real numbers
- image of function
- unit interval
- maintained by WikiProject
- WikiProject Mathematics
Sources (3)
via Wikidata · CC0
~13 min read
Encyclopedic overview
The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Different conventions concerning the value H(0) are in use. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one.
The function was originally developed in operational calculus for the solution of differential equations, where it represents a signal that switches on at a specified time and stays switched on indefinitely. Heaviside developed the operational calculus as a tool in the analysis of telegraphic communications and represented the function as 1.
Excerpted from Wikipedia’s “Heaviside step function” article, available under the CC BY-SA 4.0 licence.