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MathGroup Archive 2004

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Re: displaying images in the complex plane

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45905] Re: [mg45873] displaying images in the complex plane
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 29 Jan 2004 05:34:58 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200401281019.FAA18487@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

I highly recommend David Park's ComplexAnalysis package, which you may 
download from his web site:

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

(You may want to contact him by e-mail to see whether he has any updated 
version not yet posted there.)

The package allows not only direct visualization of a domain in the 
complex plane and, side-by-side, its image in the complex plane, but the 
corresponding thing when the complex plane is embedded in the Riemann 
sphere (and the function lifted from the plane to there).

I and my students used Park's package in my undergraduate Complex 
Analysis course this Fall.  Additional examples may be found in 
notebooks listed on the Files page at my course web site:

   http://www.math.umass.edu/Courses/Math_421/

See there, especially, IntroComplexGraphics.nb, VisualizeFunctions.nb, 
ComplexCurves.nb, VisualizeFunctions2.nb, and RiemannSphere.nb.  (And 
note that the version of Park's package in ComplexAnalysis.zip on my 
course web site is older than what's available from Park's own site.)

Nathan Moore wrote:

> Does any body have a favorite way of showing images in the complex 
> plane?  Suppose I want to represent the function Tan[z], where z = a + 
> bi, how would you display that image if you were trying to explain the 
> complex plane to your students?
> 
> Nathan Moore
> University of Minnesota Physics
> 
> 

-- 
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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