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Re: Replace Rule for LaplaceTransform

• To: mathgroup at smc.vnet.net
• Subject: [mg128719] Re: Replace Rule for LaplaceTransform
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Mon, 19 Nov 2012 19:18:59 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
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• References: <20121119090917.720F0694D@smc.vnet.net>

myLT = {
   LaplaceTransform[T_Symbol[x_, t_], t_, s_] :>
    OverTilde[T][x],
   LaplaceTransform[Derivative[n_, 0][T_][x_, t_], t_, s_] :>

    D[OverTilde[T][x], {x, n}]};

LaplaceTransform[T[x, t], t, s] /. myLT

Table[LaplaceTransform[D[T[x, t], {x, n}], t, s], {n, 0, 4}] /. myLT

Table[LaplaceTransform[D[T[x, t], {x, n}], t, s] /. myLT, {n, 0, 4}]


Bob Hanlon


On Mon, Nov 19, 2012 at 4:09 AM, KFUPM <hussain.alqahtani at gmail.com> wrote:
> Dear All
>
> How to do the following automatically using a replace rule:
>
> LaplaceTransform[T[x, t], t, s] ->
> \!\(\*OverscriptBox[\(T\), \(~\)]\)[x]
>
> and (any order of derivative)
>
> LaplaceTransform[\!\(
> \*SubscriptBox[\(\[PartialD]\), \(x, x\)]\ \(T[x, t]\)\), t, s] -> (
> \!\(\*OverscriptBox[\(T\), \(~\)]\)^\[Prime]\[Prime])[x]
>
>
> Thanks for help in advance.
>
> Regards,
>
> HMQ
>

• References:
  • Replace Rule for LaplaceTransform
    • From: KFUPM <hussain.alqahtani@gmail.com>