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Change of variables in integration

• To: mathgroup at smc.vnet.net
• Subject: [mg28266] Change of variables in integration
• From: "Loren Dill" <lorendill at mediaone.net>
• Date: Fri, 6 Apr 2001 01:53:17 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

Is there a simple way to perform a change of variables when integrating in a
symbolic form?  I'm writing a paper, and would like to express certain
results in an unevaluated dimensionless form even though I started in a
dimensional form.  I know I can check things by hand, but would prefer
Mathematica to do the work for me.  Here is a sample double integration I
want expressed in dimensionless form:

Integrate[  E^(-y u/d) p[x],{x,0,-a},{y,0,b}]

Here, x, y, a, b, p, u, and d are all dimensional.  I want to define new
dimensionless variables and parameters as follows:

xh=x/a
yh=y/b
ph[xh]=p[xh a]/p0
pe=b u/d

Here, p0 has the same dimensions as p, and pe is a dimensionless parameter.

Regards,

Loren Dill