Re: FW: Symbolic Fourier Transform

*To*: mathgroup at smc.vnet.net*Subject*: [mg26521] Re: [mg26498] FW: [mg26476] Symbolic Fourier Transform*From*: BobHanlon at aol.com*Date*: Mon, 1 Jan 2001 02:32:52 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

You did not say which version you are running. This seems to work as you expect under version 4.1. $Version "4.1 for Power Macintosh (November 2, 2000)" FourierTransform[ D[ f [t] ,t ],t,w] (-I)*w*FourierTransform[f[t], t, w] FourierTransform[ D[ f[x,t],t], t, w] (-I)*w*FourierTransform[f[x, t], t, w] LaplaceTransform[ D[ f [t] ,t ],t,s] s*LaplaceTransform[f[t], t, s] - f[0] LaplaceTransform[ D[ f [x, t] ,t ],t,s] s*LaplaceTransform[f[x, t], t, s] - f[x, 0] Bob Hanlon In a message dated 12/28/00 10:00:32 PM, BlimbaumJE at ncsc.navy.mil writes: > Sorry..I meant to say that I expected (-I w) >FourierTransform[f[x,t],t,w] not (-I w)^2,etc.. for the f[x,t] example...jb > >-----Original Message----- >From: Blimbaum Jerry DLPC [mailto:BlimbaumJE at ncsc.navy.mil] To: mathgroup at smc.vnet.net >To: mathgroup at smc.vnet.net >Subject: [mg26521] [mg26498] [mg26476] Symbolic Fourier Transform > > If you type in FourierTransform[ D[ f [t] ,t ],t,w] you get back - >I w FourierTransform[ f[t], t, w ], however if you type in > > FourierTransform[ D[ f[x,t],t], t, w] you get back >FourierTransform[ f ^(0,1)[x,t], t, w] whereas I expected (-I w)^2 >FourierTransform[f[x,t], t, w]. > > I tried the same ideas with Laplace Transform but there I got >back what I expected,namely: > > -f[0] + s LaplaceTransform[f[t],t,s] > > and > > -f[x,0] + s LaplaceTransform[ f[x,t],t,s] > > Why the differences?