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Re: One question about Diracdelta function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg46959] Re: One question about Diracdelta function
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Wed, 17 Mar 2004 02:29:10 -0500 (EST)
*Organization*: The University of Western Australia
*References*: <c388np$bo0$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
In article <c388np$bo0$1 at smc.vnet.net>,
Daohua Song <ds2081 at columbia.edu> wrote:
> hey,Group
> i want to do an integration like
> (N)Integrate[Diracdelta[f[x,y]-a],{x,min.max},{y,min,max}]
> a is a constant number, f[] is a funtion in the form of cos,sin
> It seems impossible to get exact answer by using Intergate command,
Well, it is non-trivial in general. Try the following example to see why:
Integrate[DiracDelta[Cos[x] - a], {x, b, c}]
> So is it possible to get an answer with Numerical Nintegrate?
NIntegrate will not help. You may be able to do the integration exactly
for numerical parameters. For example,
Integrate[DiracDelta[Sin[x y] - 1/2], {x, 1, 2}, {y, 0, 1}]
(You get an inverse function warning message if you try this).
> another trivial question is: Abs[Exp[ikx]....]^2,
> How can i tell the mathmatica to express it in form of Cos, Sin?
Use ComplexExpand (possibly with TargetFunctions -> {Re, Im}), e.g.,
ComplexExpand[Exp[I k x], TargetFunctions -> {Re, Im}]
Note that Conjugate only works with numerical arguments. In most
situations adding the definition
SuperStar[z_] := z /. Complex[a_,b_] :> Complex[a,-b]
(conjugation by adding a superscript * to the expression) or
OverBar[z_] := z /. Complex[a_,b_] :> Complex[a,-b]
(using an overbar instead) work nicely.
Cheers,
Paul
--
Paul Abbott Phone: +61 8 9380 2734
School of Physics, M013 Fax: +61 8 9380 1014
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Crawley WA 6009 mailto:paul at physics.uwa.edu.au
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