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MathGroup Archive 2007

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Re: fundamental Integrate question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73067] Re: fundamental Integrate question
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Thu, 1 Feb 2007 02:58:50 -0500 (EST)
  • References: <200701301144.GAA14308@smc.vnet.net><epp6te$djr$1@smc.vnet.net>

f[x_]:=1/x

Somehow it failed to appear in the original message!

Dimitris

Ï/Ç Murray Eisenberg Ýãñáøå:
> What's f[z]???
>
> dimitris wrote:
> > Consider the classical example that incorrectly gave zero in a prior
> > version of Mathematica
> > (adopted from http://library.wolfram.com/infocenter/Conferences/5832/)
> >
> > In[345]:=
> > Integrate[f[z], {z, 1 + I, -1 + I, -1 - I, 1 - I, 1 + I}]
> > Chop[N[%]]
> > Chop[NIntegrate[f[z], {z, 1 + I, -1 + I, -1 - I, 1 - I, 1 + I}]]
> >
> > Out[345]=
> > 2*I*Pi
> >
> > Out[346]=
> > 6.283185307179586*I
> >
> > Out[347]=
> > 6.2831853071795685*I
> >
> > Of course the result is correct considering the pole at origin and the
> > Residue theorem.
> >
> > Trying to understand how Mathematica applies the Newton-Leibniz
> > formula I just want to know if
> > I am right below:
> >
> > In[511]:=
> > ((F[z] /. z -> 1 - I) - F[z] /. z -> -1 - I) + ((F[z] /. z -> 1 + I) -
> > F[z] /. z -> 1 - I) +
> >   ((F[z] /. z -> -1 + I) - F[z] /. z -> 1 + I) + (Limit[F[z], z -> -1,
> > Direction -> -I] - F[z] /. z -> -1 + I) +
> >   ((F[z] /. z -> -1 - I) - Limit[F[z], z -> -1, Direction -> I])
> >
> > Out[511]=
> > 2*I*Pi
> >
> > Thanks for any response!
> >
> > Dimitris
> >
>
> --
> Murray Eisenberg                     murray at math.umass.edu
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower      phone 413 549-1020 (H)
> University of Massachusetts                413 545-2859 (W)
> 710 North Pleasant Street            fax   413 545-1801
> Amherst, MA 01003-9305


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