Re: Advanced symbolic Integration using Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg59656] Re: Advanced symbolic Integration using Mathematica
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Tue, 16 Aug 2005 04:39:44 -0400 (EDT)
- Organization: The University of Western Australia
- References: <ddpt6m$orm$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <ddpt6m$orm$1 at smc.vnet.net>, mike_in_england2000 at yahoo.co.uk
wrote:
> I am going to be demonstrating Mathematica to a group of people who
> have never seen the package before and I wanted to give an impression
> of the power and range of its symbolic integration.
>
> I have already included simple well known things such as the Guassian
> integral
> Integrate[Exp[-x^2], {x, -Infinity, Infinity}]
>
> Integrals involving Bessel functions, eg
> Integrate[BesselJ[1, z], z]
>
> What I am looking for now is a few relatively simple *looking*
> integration problems that, if done by hand, would require the use of
> advanced techniques (such as contour integration) or would take pages
> of working out or preferably both.
>
> Does anyone out there know of any such integration problems that can
> help contriubute to the Gee-Whizz factor?
Have a look in the Help Browser under
Demos | Formula Gallery
There are some nice examples there. One example I like is
Assuming[Element[r, Reals],
Integrate[BesselJ[0, k r]/(k^2 + 1)^(3/2), {k, 0, Infinity}]]
Quite a simple integral but one with a rather complicated representation.
I think that it is good idea to use TraditionalForm for such talks, for
output at least, because this shows the power of Mathematica's
typesetting and also, to an audience unfamiliar with Mathematica, it
produces output that is more readily understandable.
Cheers,
Paul
--
Paul Abbott Phone: +61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
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http://InternationalMathematicaSymposium.org/IMS2005/