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Re: symbolic approximation (formular manipulation)

• To: mathgroup at smc.vnet.net
• Subject: [mg55044] Re: symbolic approximation (formular manipulation)
• From: David Bailey <dave at Remove_Thisdbailey.co.uk>
• Date: Thu, 10 Mar 2005 05:25:04 -0500 (EST)
• References: <d0mnef$71b$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Zhe Hu wrote:
> A formula in electrical engineering can be simplified after assuming,
> e.g. R1<<R2, within 10% error tolerance.
> 
> How this kind of "simplify" or approximation can be performed by Mathematica?
> 
> For example, R1<<R2, R2<<R3
> 
> R1+R2                      R2                                      R2
> ---------------  --->  ------------------  ---------> ------------------
> R1(R2+R3)               R1(R2+R3)                       R1 R3
> 
> 
> 
> I thought about replacing: R1->0.00001*R2, but that would eliminate R1
> completely from the formula (denumerator), which is not favorable in
> some cases.
> 
One answer is to replace R1->R2*eps1 and do a series expansion in eps1 
and drop the higher terms. Then do the same with r2->R3*eps2 - because 
you have used symbolic small quantities, you can still recover your 
original variables.

David Bailey
dbaileyconsultancy.co.uk