Derivatives -n.1

[Camillo]

a) Calculate the derivative of the restriction to $ (0,3) $ of the function $ u(x) =[x]$ ( integer part of $x$ ).

b) Express in terms of Heaviside functions the restrictions to $(0,+oo) $ of the function $ u(x) =[x]$ ( integer part of $x$ ) and calculate its derivative.

[Camillo]

Correct answers.
Both names are used for the same function : my impression is that in math texts is used Heaviside function , while in applications like telecomunications is used step function.

In
http://mathworld.wolfram.com/

is used Heaviside step function


http://mathworld.wolfram.com/HeavisideStepFunction.html

It can also be named as characteristic function of the interval $[0, +oo)$.

[Kroldar]

a) $delta(x-1) + delta(x-2)$

b) $f(x) = sum_(k=1)^(+oo) H(x-k)$ where $H(.)$ is Heaviside function
$f'(x) = sum_(k=1)^(+oo) delta(x-k)$


On the books I've studied, Heaviside function is usually called "step function" or simply "step" and its symbol is $u(.)$ (and not $H(.)$).