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MathGroup Archive 1998

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Re: Multi-Variate Taylor Series Expansions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14723] Re: [mg14718] Multi-Variate Taylor Series Expansions
  • From: "Kevin J. McCann" <kevinmccann at Home.com>
  • Date: Wed, 11 Nov 1998 17:53:31 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Try Series:

Normal[Series[f[x,t],{x,x0,2},{t,t0,2}]]

%/.(x-x0)->dx/.(t-t0)->dt

%//Expand

Kevin


-----Original Message-----
From: Tom Bell <tombell at stanford.edu> To: mathgroup at smc.vnet.net
Subject: [mg14723] [mg14718] Multi-Variate Taylor Series Expansions


>
>Is there a function in Mathematica that will do multi-variate Taylor
>series
>
>expansions?  For example, suppose I have
>
>function = F(x + dx, t + dt)
>
>then the expansion to second order about (x,t) should look something
>like
>
>expansion = F(x,t) + dx D(F,x) + dt D(F,t) + (1/2) dx^2 D(F,{x,2}) +
>
>    dx dt D(F,{x,t}) + (1/2) dt^2 D(F,{t,2}) + O(dx^3) + O(dt^3)
>
>The situation gets a little more complicated: the function may look like
>
>F(x + G(x + dx, t + dt), t + dt) and so on, so that the expansion should
>be
>
>recursive.  After expanding F, the function should keep going back and
>expending G until no
>
>further expansions can be done.
>
>Please reply to tombell at stanford.edu, and thanks in advance for your
>help.
>
>---------------------------------------------------------------- 
>Thomas (Tom) Bell               
>Gravity Probe-B, H.E.P.L. tombell at stanford.edu
>Stanford University 136D Escondido Village          
>Stanford, CA
>94305-4085 Stanford, CA 94305              650/725-6378 (o)
>650/497-4230 (h)                650/725-8312 (fax)
>



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