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Re: Mathematica not simplifying Laplace transforms

• To: mathgroup at smc.vnet.net
• Subject: [mg61453] Re: [mg61334] Mathematica not simplifying Laplace transforms
• From: Devendra Kapadia <dkapadia at wolfram.com>
• Date: Wed, 19 Oct 2005 02:17:03 -0400 (EDT)
• References: <200510160417.AAA22522@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On Sun, 16 Oct 2005, Roger wrote:

> Hi.
> I'm just testing out Mathematica 5.2 and I'm having a few problems.
>
> 1) How do I get Mathematica to simplify
>
> LaplaceTransform[Exp[t]*f[t], t, s]
>
> I expect it to say something like
>
> LaplaceTransform[f[t], t, -1 + s]
>
> but it just repeats the input expression.
>
> Basically, how do I get it to behave like on this page:
> http://www.ma.iup.edu/projects/CalcDEMma/laplace/laplace1.html
>
> 2) This might be related, how do I define the domain of a variable?
> Like making the variable "t" a positive real number.
>
> Thanks.
>
> Regards,
> Roger
>
Hello Roger,

Thank you for reporting the problem with using the "shifting property"
(multiplication by Exp[t]) in the LaplaceTransform.

It appears that this functionality was lost when LaplaceTransform
was moved from being a standard add-on package to a kernel function
in Mathematica 4. (You will notice that the webpage

    http://www.ma.iup.edu/projects/CalcDEMma/laplace/laplace.html#laplace1

requires the Calculus`LaplaceTransform` package to be loaded, which is
not necessary in Mathematica 5.2).

At present, we do use the shifting property internally to simplify
the evaluation of Laplace transforms in specific cases where the transform
of f[t] exists, but there seems to be no workaround when this returns
unevaluated. We hope to restore this functionality in a future version.

As noted by others, you can use the Assuming function to define the domain 
of a variable. Here is an example for this function:

========================================================
In[1]:= $Version

Out[1]= 5.2 for Linux (June 27, 2005)

In[2]:= Assuming[x > 0, Simplify[Sqrt[x^2]]]

Out[2]= x

In[3]:= Assuming[x < 0, Simplify[Sqrt[x^2]]]

Out[3]= -x

=====================================================

We apologize for the confusion caused by the problem with
LaplaceTransform.

Sincerely,

Devendra Kapadia,
Wolfram Research, Inc.

• References:
  • Mathematica not simplifying Laplace transforms
    • From: "Roger" <rogerbrent2@gmail.com>