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MathGroup Archive 2007

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Re: question (for Mathematica 6!)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75555] Re: question (for Mathematica 6!)
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 5 May 2007 05:58:12 -0400 (EDT)
  • References: <f1ept5$4n1$1@smc.vnet.net>

Hi,

{HeavisideTheta[#], UnitStep[#]} & /@ {-0.1, 0, 0.1}

gives

{{0, 0}, {HeavisideTheta[0], 1}, {1, 1}}

the Heaviside Theta function is a distribution, i.e.
it only exist/is defined in expressions like

Integrate[HeavisideTheta[x]*f[x],{x,-a,a}]

and it has no defined value at 0 (look for DiracDelta[]
that is also a distriution).

The UnitStep[] function is defined everywhere on the
axis and you don't need an integral to define it

Regards
   Jens

dimitris wrote:
> I don't have a copy of Mathematica 6 but having spent much time
> reading the online documentation (not only because of curiosity!) I
> have one question...
> 
> Can somebody explain me the introduction of the HeavisideTheta
> function
> 
> http://reference.wolfram.com/mathematica/ref/HeavisideTheta.html
> 
> in version 6?
> 
> Note that the UnitStep function is still here
> 
> http://reference.wolfram.com/mathematica/ref/UnitStep.html
> 
> Dimitris
> 
> 


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