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Topic: Replace Rule for LaplaceTransform
Replies: 1   Last Post: Nov 19, 2012 7:19 PM

 Bob Hanlon Posts: 906 Registered: 10/29/11
Re: Replace Rule for LaplaceTransform
Posted: Nov 19, 2012 7:19 PM

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@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
>