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We're studying complex analysis transformations in the university right now (linear fractional transformation, Joukowsky transform, exponents, their compositions, etc).

I'm looking for an application which can, given a curve in a form of either equation on complex number or equation on coordinates (like |z-i|<2) and a transformation (like w(z)=z^2+1/z) show me what this curve will turn into after applying the transformation.

It'd also be very useful if the tool can also show which areas/points are transformed into which. Interactivity is good to have, but something like Octave with pre-written program to do that kind of plotting is also ok.

I'm looking for a software or web application which I can use for free on my personal laptop. Free license "for educational purposes" is acceptable as long as it does not require the university to have .edu-address, detailed transcripts or contract with the university (like MSDN AA). I'm not interested in try-before-buy or monthly subscriptions, although they may be useful for other users, so I think they worth sharing anyway.

I know about Matlab, Mathematica and they probably can do that kind of thing, but they are not free. I've also tried WolframAlpha but it looks like I cannot specify which curve or point to transform.

I'm looking for either web software, Windows software or Linux software.

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I would suggest the combination of python, numpy/scipy, matplotlib & jupyter.

All of the above software elements:

  • Fit together nicely
  • Can produce submission ready results
  • Are Free, both gratis & Open Source for personal, acedmic, professional & business use.
  • Work on a variety of OS platforms
  • The code can be expected to work across those platforms without modification.

You can see the sort of results that can be obtained here. enter image description here The above Content under Creative Commons Attribution license CC-BY 4.0, code under MIT license (c)2015 L.A. Barba, Pi-Yueh Chuang.

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