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) >