Q: How do you define the derivatives of the Heaviside, Sign, Absolute Value, and Delta functions? How do they relate to one another?

Q: How do you define the derivatives of the Heaviside, Sign, Absolute Value, and Delta functions? How do they relate to one another?

The absolute value function flips the sign of negative numbers, and leaves positive numbers alone. The Heaviside function is very similar; 1 for positive numbers and 0 for negative numbers. By the way, the Heaviside function, rather than being named after its shape, is named after Oliver Heaviside, who was awesome. But that sounds a bit like the delta function; zero everywhere, except for an infinite spike at x=0. Answer Gravy: The Dirac delta function really got under the skin of a lot of mathematicians.

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