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Re: Re: Re: Suggestion: Visualization of complex functions with Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg44909] Re: [mg44899] Re: Re: Suggestion: Visualization of complex functions with Mathematica
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 8 Dec 2003 02:29:17 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <bqkb3v$hkt$1@smc.vnet.net> <200312051031.FAA09156@smc.vnet.net> <bqs93e$i15$1@smc.vnet.net> <200312071103.GAA29625@smc.vnet.net>
• Reply-to: murray at math.umass.edu
• Sender: owner-wri-mathgroup at wolfram.com

You might add to your list the ComplexAnalysis application by David Park at:

   http://home.earthlink.net/~djmp/Mathematica.html

I've been using it in an undergraduate complex analysis course this 
semester and have found it VERY instructive.

In case anybody wants to examples beyond those in Park's notebooks, you 
may take a look at some of the notebooks at

   http://www.math.umass.edu/Courses/Math_421/Files/files.html

namely, the following files:

   IntroComplexGraphics.nb
   CartesianPolarForms.nb
   VisualizeFunctions.nb
   ComplexCurves.nb
   VisualizeFunctions2.nb
   RiemannSphere.nb
   ExponentialFunction.nb
   Sine.nb
   Poles.nb


Peltio wrote:

> "Murray Eisenberg" wrote
> 
> 
>>What is the correct URLs for the ones listed below: www.kfunigratz.ac.at
>>is not being found.
> 
> 
> I apologize.
> The correct URL (I checked it out now) is
> http://www.kfunigraz.ac.at/imawww/vqm/pages/dlgraph.html
> 
> While searching the web for the correct address, I've also found the
> following packages that can be used to plot complex functions (I'm sure that
> there are many more). Some are new to me, but the original poster might find
> them interesting enough to try'em out.
> They can be reached by using the author name, the package name in Google
> (www.google.com) For example fill in the search field with "ComplexPlot.m"
> or "complex mathematica filetype:m".
> 
> Complex.m by Goeran Andersson
> http://www.funet.fi/pub/sci/math/mathematica/Analysis/Complex.m
>     *zListPlot[ zlist, opts] pointplots the complex numbers in zlist.
>     *zwPlot[ z, w, {t, tmin, tmax}, opts] plots the complex mapping
>      w=f(z), z=z(t).
> 
> ComplexPlot.m by Jeff Olson
> http://www.ph.utexas.edu/~jdolson/math/ComplexPlot.m
>     *ComplexPlot[func, {fx, fy}, {t, tmin, tmax}]
>     *ComplexListPlot[{z1, z2, ...}] plots a list of complex numbers.
>     *ComplexVectorPlot[func, {xmin, xmax}, {ymin, ymax}]
>     *ComplexPartialPlots[func, {xmin, xmax}, {ymin, ymax}]
>     *ComplexColorPlot[func, {xmin, xmax}, {ymin, ymax}]
>     *ComplexContourPlot[func, {xmin, xmax}, {ymin, ymax}]
>     *CartesianMap[f, {x0, x1, (dx)}, {y0, y1, (dy)}] plots the image
>      of the cartesian coordinate lines under the function f.
>     *PolarMap[f, {r0:0, r1, (dr)}, {phi0, phi1, (dphi)}] plots the
>      image of the polar coordinate lines under the function f.
> 
> ComplexPlot3D by Kevin McIsaac
>    *ComplexPlot3D[fn, {x, x0, x2, (dx)}, {x, x0, x2, (dx)}, (options)]
>    Plots in the complex plane. The absolute value is represented
>    by the height and the phase is represented by the color
> 
> ComplexMap by Roman Maeder
>     *CartesianMap[f, {x0, x1, (dx)}, {y0, y1, (dy)}] plots the image
>      of the cartesian coordinate lines under the function f.
>     *PolarMap[f, {r0:0, r1, (dr)}, {phi0, phi1, (dphi)}] plots the
>     image of the polar coordinate lines under the function f.
> 
> Transform2DPlot by Xah Lee
> http://www.xahlee.org/SpecialPlaneCurves_dir/MmaPackages_dir/Transform2DPlot
> _dir/Transform2DPlot.m
>     This package exports the function Transform2DPlot and
>     Transform2DGraphics that plot the image of the plane under
>     arbitrary transformation function f:R^2->R^2 or f:C^1->C^1.
>     It can be easily adapted to make it plot conformal maps.
>     It is possibile to write a shell that calls the procedures with a
>     syntax similar to that of ComplexMap. (years ago I wrote one,
>     only a few lines long - no big deal since Xah Lee's procedures do
>     it all. If someone is interested, though, and has already
>     downloaded the original package by Xah Lee let me know and
>     I'll send it to them)
> 
> ComplexMapPlot by Theodore W. Gray and Jerry Glynn
>     This one is included in their book "Exploring Mathematics with
>     Mathematica", Addison-Wesley, 1991. I don't think it is
>     available on the web. I had found a reference to it in a gallery
>     of complex functions (I saved it in rtf format without the
>     pictures!!! How smart : )). But if the original poster has access to
>     the book he can find out if what it does suits him.
> 
> cheers,
> Peltio
> Invalid address in reply-to. Crafty demunging required to mail me.
> 
> 

-- 
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

• References:
  • Re: Suggestion: Visualization of complex functions with Mathematica
    • From: "Peltio" <peltio@twilight.zone>
  • Re: Re: Suggestion: Visualization of complex functions with Mathematica
    • From: "Peltio" <peltio@twilight.zone>