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 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul