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Re: What is the problem? There are no images and no wrong reports for

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112364] Re: What is the problem? There are no images and no wrong reports for
  • From: peter <justwanglunwei at gmail.com>
  • Date: Sat, 11 Sep 2010 05:43:15 -0400 (EDT)
  • References: <i6a5dp$kim$1@smc.vnet.net>

On Sep 9, 4:21 pm, Bill Rowe <readn... at sbcglobal.net> wrote:
> On 9/7/10 at 2:02 AM, justwanglun... at gmail.com (peter) wrote:
>
>
>
> >Hello Mathematica community, I really need some help.... I realized
> >there are some mistakes in this program, but I can't find out what
> >it is,  I keep trying for weeks, still there are some problem, I
> >never used Mathematica before
> >a==Exp[(-2r^2)/3]; b==BesselJ[0,(r*Sqrt[x^2+y^2])/0.8]; c==r=
^2=
> ;
> >d==5a;
> >Plot[Abs[Integrate[r*b*a*Exp[-I(c+d)]dr,{r,0,=E2=88=9E}]]^2,{x,-0.0
> >,0.01}, {y,-0.01,0.01}]
> >=EF=BC=88I is Complex i=EF=BC=89
>
> Your email is coming through somewhat garbled. The best way to
> post code in email is to select the cell in Mathematica you want
> to post and ensure the format of that cell is in InputForm
> before doing the copy/paste into email. You can make any cell be
> in InputForm by selecting the cell then going to the Cell menu
> selecting ConvertTo->InputForm. On a Mac, this also has a
> shortcut key of cmd-shift-I. There should be a similar shortcut
> on other platforms. Also, it is a good idea to avoid using
> special characters such as Greek symbols for something to be
> posted. Doing the above will make your post easier to read and
> avoid the problem being seen in your post.
>
> I am going to have to guess a bit as to the source of your
> problem. Judging by what appears to be part of an error message
> it looks like you might be using a complex variable for the
> upper integration limit. But since this part is garbled, I
> cannot be sure about this or if this is part of the issue.
>
> It also appears you are explicitly using dr to be have the usual
> meaning this has in a text. That portion of the integral should
> not be used when doing integration with Mathematica. The dr term
> will be seen by Mathematica as a separate variable with no
> dependence on r multiplying the other terms in the integrand.
>
> The Integrate command should be outside the Plot command or you
> should use Evaluate to force evaluation of the integral before
> Plot tries to actually plot the integral.
>
> That is
>
> g[x_] = Integrate[y Exp[y], {y, 0, x}];
> Plot[g[x], {x, 0, 2}]
>
> will generate a plot reasonably quickly
>
> But
>
> Plot[Integrate[y Exp[y], {y, 0, x}],{x, 0, 2}]
>
> will also create the same plot but will run much slower since
> the integral is being evaluated repeatedly for every value of x
> Plot uses to create the graphic.
>
> Note, hear I used Set (=) not SetDelayed (:=) when defining g.
> Had I used SetDelayed here, there would have been no improvement
> in time required to generate the plot.
>
> Also, for this example, I used an integral that has a closed
> form solution. For integrals where no closed form solution
> exists there won't be much to gain by having the integral
> outside the Plot command. But in these cases it is probably
> better to use NIntegrate rather than Integrate.

i'm sorry for the garbled...thank you for your advise,that's a lot
help...


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