The Dirac command takes as input a number.
Dirac returns infinity if the number is 0, it
returns 0 otherwise.
Dirac represents the distribution which is the derivative of the Heaviside function. This means that
∫ |
| Dirac(x) dx = 1 |
and, in fact, ∫ab Dirac(x) dx is 1 if [a,b] contains 0 and the integral is 0 otherwise. The defining property of the Dirac distribution is that
∫ |
| Dirac(x) f(x) dx = f(0) |
and consequently
∫ |
| Dirac(x−c) f(x) dx = f(c) |
as long as c is in [a,b].
Input:
Output:
Input:
Output: