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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?