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 0.5 when x is 0.
To type Φ, press F, Ctrl+G
The above functions are special cases of the if function.
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.
Arguments
• m, n are dimensionless integers.
• x is a real scalar or vector.