What is the condition for the Jacobian transformation when changing variables?

[femas]

Hi,

Assume that I have f(u,v,w,h) du dv dw dh and I need only to change three variables (u, v, w) say to other variables called (s, r, t) and keep h as is it is

So my question can I write this as

f(u,v,w,h) du dv dw dh = G(r,s,t,h) J(r,s,t) dr ds dt dh

where J is jacobian transformation. What is the condition that has to be satisfied?

 

[mathman]

You can always do it (as long as the transformation is nice). If you want to be completely consistent, let h' (new) = h (old) so you will be working with a four variable transformation.

 

[femas]

Thanks for your reply!