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.