Go to the Mathematica documentation for the HeavysideTheta
function. There is an example for integration:
Integrate[HeavisideTheta'''[x - a] f[x], {x, -Infinity, Infinity},
Assumptions -> a ∈ Reals]
The options Assumptions
works with every built-in of Mathematica.
Mathematica allows the $Assumptions
shell variable.
Simply set:
$Assumptions = x∈Reals
in the complete notebook or in a Block
.
In the notebook set $Assumptions = True
if not needed anymore.
Since Mathematica infers the domain from the input, just input Reals
only will do usually enough work. Check if the input variables and constant is done with Elements
Following the idea:
unbreakableHeavisideTheta[x_] := HeavisideTheta[Re[x]]
Re
makes every complex number real ignoring the complex part of it.