Definition talk:Heaviside Step Function

From ProofWiki
Jump to navigation Jump to search

D'oh! I understand what you mean now. --prime mover (talk) 13:01, 13 May 2014 (UTC)

I still wonder whether we need to explain why the value of a function at the point of discontinuity is unimportant in the context of integral calculus -- from what I remember from my analysis days, this subtlety was usually glossed over. It would be nice to write a page which specifies in detail exactly why. We may have to do so anyway, when we cover the behaviour of the impulse function, as it stretches the boundary of that statement. --prime mover (talk) 13:11, 13 May 2014 (UTC)


I'm convinced now I made up the $\mu$ notation after misreading a lowercase $u$. I can't find a single source that uses it; Deprima and Khan Academy both use $u$, and those were my references when I made the page.

So I should go and change the notation to one of the standard $u$, $H$, or $\theta$. The question is, which do we prefer? I asked my professor and he said that all are common, but $\theta$ is the one he sees physicists use the most. OTOH, with $\mathsf{Pr} \infty \mathsf{fWiki}$'s philosophy that we try to use people's names when possible, $H$ is the most reminiscent of the function's eponym. --GFauxPas (talk) 09:28, 15 December 2016 (EST)

1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables uses $\mathcal U$ and calls it Heaviside's unit function. 1986: Kurt Arbenz and Alfred Wohlhauser: Advanced Mathematics for Practicing Engineers uses just $\mathrm u$ and calls it the unit step function. 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions uses $u$. I'm dismayed that I can't find more books on my shelves that mention it. I'm sure I must have lost a load.
In short, $u$ everywhere, never seen $\theta$ and not sure I've ever seen $H$ either. My recommendation is to go with $u$ or a variant as it seems most common. I would change it on the main page and go through as and when you find it convenient to replace all the $\mu$s with $u$s. Are there many? I haven't looked. --prime mover (talk) 15:13, 15 December 2016 (EST)
Update: I have a source: 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) which uses $H$. But we may as well stick with $u$ now. --prime mover (talk) 10:48, 14 March 2020 (EDT)