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5.8.10 The Dirac distribution: Dirac

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



−∞
 δ(x) dx = 1 

and, in fact,

b


a
 δ(x) dx =   


      1if  0 ∈ [a,b]
      1otherwise

The defining property of the Dirac distribution is that

  


−∞
 δ(x) f(x) dx = f(0)

and consequently

  
b


a
 δ(xc)f(x) dx = f(c)

as long as c is in [a,b].

The Dirac command represents the Dirac distribution.

Examples.


If you have Dirac compute a value:


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