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change of variables in PDE?

• To: mathgroup at smc.vnet.net
• Subject: [mg8834] change of variables in PDE?
• From: Geoffrey Simms <gdsimms at uiuc.edu>
• Date: Mon, 29 Sep 1997 02:40:00 -0400
• Organization: University of Illinois at Urbana-Champaign
• Sender: owner-wri-mathgroup at wolfram.com

I hope this isn't too trivial a question...

I am trying to change variables in a PDE

f[x_,y_] -> F[X,Y]

where the new variables and functions are defined like, e.g.:

X = x^2 + y
Y = 2 + x y
F = x f

I would like Mathematica to recognize f and all of its partial
derivatives, applying the chain rule where necessary, etc. to a PDE
given in terms of f, x, and y, returning the PDE in terms of F, X, and
Y, with all derivatives fixed accordingly.

It seems that this would be a common request, and yet in all my searcing
I haven't found a way to do this. Is there a package anyone knows about
that does this?

Thank you,
Geoff Simms