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RE: Change of Variables

• To: mathgroup at smc.vnet.net
• Subject: [mg32523] RE: [mg32509] Change of Variables
• From: "David Park" <djmp at earthlink.net>
• Date: Fri, 25 Jan 2002 02:57:54 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

John,

Here is one method.

planck = 2*Pi*c^2*h/lambda^5*(E^(h*c/(lambda*k*T)) - 1)^(-1);

Solve[x == h*(c/(lambda*k*T)), lambda][[1,1]]
lambda -> (c*h)/(k*T*x)

planck /. lambda -> (c*h)/(k*T*x)
(2*k^5*Pi*T^5*x^5)/(c^3*(-1 + E^x)*h^4)

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 

> From: John S [mailto:bosniajohns at hotmail.com]
To: mathgroup at smc.vnet.net
> 
> Hello,
> 
> I would greatly appreciate any help with the following problem.  
> I am trying
> to perform a change of variable in a function/definition so that I can
> integrate it.  In particular, I want to take Planck's Radiation Law:
> 
> planck=2*Pi*c^2*h/lambda^5*(E^(h*c/(lambda*k*T))-1)^(-1)
> 
> and substitute x=h*c/(lambda*k*T) and integrate wrt lambda from 0 to
> infinity.  I tried using replace, but that does not seem to try to
> manipulate the function in terms of x, but simply seek out the 
> replacement,
> and if it exists, perform it.
> 
> An even simpler example is the following:
> 
> test=v/c
> Replace[test^2,v/c -> beta]
> 
> does not yield beta^2, but rather v^2/c^2.
> 
> Again, any and all help would be greatly appreciated.
> 
> 
>