7.3.10 Dirac distribution

The Dirac δ distribution is the distributional derivative of the Heaviside function. This means that

and, in fact,

The defining property of the Dirac distribution is that

and consequently, for c∈[a,b],

The Dirac command represents the Dirac distribution.

• Dirac takes one mandatory argument and one optional argument:
  • x, a symbol or an expression.
  • Optionally, n, a nonnegative integer.
• Dirac(x ⟨,n ⟩) returns δ⁽ⁿ⁾(x), where δ⁽ⁿ⁾ is the nth derivative of δ.

Note that x can be a real number, for which Dirac returns 0 if x≠ 0 and ∞ otherwise. However, since δ is a distribution, not a function, computing its value at a point makes little sense.

Examples