Re: One question about Diracdelta function

• To: mathgroup at smc.vnet.net
• Subject: [mg46992] Re: One question about Diracdelta function
• From: Olaf Rogalsky <rogalsky at physik.uni-erlangen.de>
• Date: Fri, 19 Mar 2004 01:35:45 -0500 (EST)
• References: <c388np\$bo0\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Daohua Song wrote:
>     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, So
> is it possible to get an answer with Numerical Nintegrate?
No, but with a little bit of thought (or an elementary textbook),

Integrate[Diracdelta[f[x,y]-a],{x,min.max},{y,min,max}] =

Sum[1/Abs[D[f[x_i, y_i], x, y]], {i, n}], where

{x_i, y_i | i=1..n} is the set of all solutions to

f[x,y]==a,  with x in [xmin,xmax] and y in [ymin,ymax]

--
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I Dr. rer. nat. Olaf Rogalsky     Institut fuer Theoretische Physik I
I                                 Universitaet Erlangen-Nuernberg   I
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