Re: Advanced symbolic Integration using Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg59653] Re: Advanced symbolic Integration using Mathematica
- From: "James Gilmore" <james.gilmore at yale.edu>
- Date: Tue, 16 Aug 2005 04:39:33 -0400 (EDT)
- Organization: Yale University
- References: <ddpt6m$orm$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
In addition to the Guassian integral, use:
In[266]:=
Integrate[Exp[-x^n], {x, -Infinity, Infinity}, Assumptions -> n > 0]
They will be much more impressed seeing the integration with a general
argument, and a (sensible) condition on n.
On a sidebar, everyone I have talked with dislikes the elaborate conditions
Integrate generates these days. Warn your group about these to be on the
safe side. I have thought since 5.0 that Integrate has become too general.
Perhaps a function, IntegrateNoNosense, which has only the bare essentials
of Integrate, is required in a future release of Mathematica. Then new and
experienced users do not have to deal with these annoyances constantly.
Cheers
James Gilmore
Graduate Student
Department of Physics
Yale University
New Haven, CT 06520 USA
Email: james.gilmore at yale.edu
URL: <http://pantheon.yale.edu/~jbg39/>
<mike_in_england2000 at yahoo.co.uk> wrote in message
news:ddpt6m$orm$1 at smc.vnet.net...
> Hi
>
> 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?
>
> Looking forward to any replies.
>
> Mike
>