Kronecker Delta and Heaviside Step Functions |
δ(m, n) Returns 1 if m = n, otherwise, returns 0. (To type δ, press d [Ctrl] g.)
Φ(x) Returns 0 for negative values of x, 1 for positive values of x, and .5 when x is 0. (To type Φ, press F [Ctrl] g.)
Arguments:
- m, n are dimensionless integers.
- x is a real scalar or vector.
Notes:
- Integrating discontinuous functions over an interval containing the discontinuity results in an error. Instead, divide the region of integration into two parts, integrate over each separately, and add the result. For the same reason, the derivative of these functions is undefined at 0.
- These are special cases of the if function.