Heaviside step function
The Heaviside step function is the function defined as
Here, there are many conventions for the value at . The motivation for setting is that we can then write as a function of the signum function (see this page (http://planetmath.org/SignumFunction)). In applications, such as the Laplace transform, where the Heaviside function is used extensively, the value of is irrelevant. The Fourier transform of heaviside function is
where denotes the Dirac delta centered at . The function is named after Oliver Heaviside (1850-1925) [1]. However, the function was already used by Cauchy[2], who defined the function as
and called it a coefficient limitateur [3].
References
- 1 The MacTutor History of Mathematics archive, http://www-gap.dcs.st-and.ac.uk/ history/Mathematicians/Heav iside.htmlOliver Heaviside.
- 2 The MacTutor History of Mathematics archive, http://www-gap.dcs.st-and.ac.uk/ history/Mathematicians/Cauc hy.htmlAugustin Louis Cauchy.
- 3 R.F. Hoskins, Generalised functions, Ellis Horwood Series: Mathematics and its applications, John Wiley & Sons, 1979.
Title | Heaviside step function |
---|---|
Canonical name | HeavisideStepFunction |
Date of creation | 2013-03-22 13:46:14 |
Last modified on | 2013-03-22 13:46:14 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 8 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 30-00 |
Classification | msc 26A06 |
Synonym | Heaviside function |
Related topic | SignumFunction |
Related topic | DelayTheorem |
Related topic | TelegraphEquation |