Why is the Heaviside step function named after Heaviside?

The Heaviside step function is usually defined as

$$\theta(x)=\left\{\begin{array}{ll}0&\text{if }x<0\\\tfrac12&\text{if }x=0\\1&\text{if }x>0.\\\end{array}\right.$$

It is remarkably simple and doesn't take a lot of work to define, though if used properly it does play an important role in a number of fields, including notably the study of distributions. It is nevertheless named after Oliver Heaviside.

What was his involvement with this function, and why does it merit this honour? In particular, I'm looking for well-documented sources which show his use of the concept and the context in which he used it. Ideally, I would also like references to the initial works which associate his name with the function, and their reasons for doing so.

• He invented it. – Jiminion Feb 17 '15 at 18:38
• Check out the biography by Paul Nahin. – Jiminion Feb 18 '15 at 12:48
• @Jiminion Apologies, but that hardly counts as "references". Could you be more specific? – Emilio Pisanty Feb 18 '15 at 12:52
• "Electromagnetic induction and its propagation". 1885-1887. It was in his earlier works. – Jiminion Feb 18 '15 at 13:02
• myreckonings.com/wordpress/2007/12/07/… for some links to original papers by Heaviside – Tom Copeland Mar 5 '15 at 3:05