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Change of variables in partial derivatives

POSTED BY: Alberto Silva Ariano
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This package ("MoreCalculus`") is a very simple one, it only introduces DChange function and there is not built-in DChange symbol so you don't need to worry about it.

Will there ever be a built-in DChange symbol? Who knows, maybe, maybe not, I suppose WRI will pick a better name for such a function.
POSTED BY: Kuba Podkalicki

Dear users Tim Laska and Kuba Podkalicki:

Thank you for your answers. Now, a few comments:

1) Tim Laska suggestion works very fine for rescaling transformations, but I'm not sure if it is enough for "mixed variables" transformations like:

          t0 = t - x/u ( t0, t = time, x = lenght, u = velocity)

As the new time coordinate (useful for example to simplify some wave equations) mixes the "original" x and t coordinates.

2) The function DChange of Kuba Podkalicki looks just like what I was looking for, but I'm afraid of some software compatibility issues if I download the package. Could it cause some problems/damage to the original Mathematica language, specially for newer versions like Mathematica 12 (not to mention future versions in coming years)?
POSTED BY: Alberto Silva Ariano

Maybe this helps

Regards M.I.
POSTED BY: Mariusz Iwaniuk

It seems that my old code still works so you can do:

DChange[ D[f[t, z], {{t, z}}],  {z0 == z/L, t0 == t u /L}, {t, z}, {z0, t0}, f[t, z]]

{(u (f^(0,1))[z0,t0])/L,(f^(1,0))[z0,t0]/L}

You can read how to install DChange and use it from: Analogue for Maple's dchange - change of variables in differential expressions
POSTED BY: Kuba Podkalicki

Setting up the derivative as an anonymous function might help.

newD = D[#, {{t, z}}] &;
newD@f[t u/L , z/L]
(*{(u*Derivative[1,0][f][(t*u)/L,z/L])/L,Derivative[0,1][f][(t*u)/L,z/\
L]/L}*)
POSTED BY: Tim Laska
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