"Greg Heath" <heath@alumni.brown.edu> wrote in message <j1amts$daa$1@newscl01ah.mathworks.com>...
> "evan um" wrote in message <j19n5k$h2u$1@newscl01ah.mathworks.com>...
> > Hi,
> >
> > I hope that I can have your comments on how to correctly implement symbolic laplace transform. For example, my Laplace transform matlab script follows.
> >
> > syms t sig t0;
> > f=2/sqrt(3*sig)/pi^0.25*(1(tt0)^2/sig^2)*exp((tt0)^2/2/sig^2);
> > f_LFTed=laplace (f)
> >
> > I expect the results such as f_LFTed=function of only s. However, the result is given as
> > (9007199254740992*3^(1/2)*(sig^2*laplace(1/exp((t^2  2*t*t0 + t0^2)/(2*sig^2)), t, s)  t0^2*laplace(1/exp((t^2  2*t*t0 + t0^2)/(2*sig^2)), t, s) + 2*t0*laplace(t/exp((t^2  2*t*t0 + t0^2)/(2*sig^2)), t, s)  laplace(t^2/exp((t^2  2*t*t0 + t0^2)/(2*sig^2)), t, s)))/(17987404344949797*sig^(5/2))
> > In other words, the result still has laplce transfrom function. I can not evaluate the result. Can you explain how to get the complete Laplace transform result? In advace, thank you very much for reading this question.
> >
> > Evan
>
> Have you tried just
>
> (1t^2)*exp(t^2)
This is what i get from Matlab 6.5
close all, clear all, clc
syms t
f = (1t^2)*exp(t^2);
F = laplace (f)
fhat = ilaplace(F)
% Command line Answers
%
% F = 1/4*pi^(1/2)*exp(1/4*s^2)*erfc(1/2*s)...
% 1/8*pi^(1/2)*s^2*exp(1/4*s^2)*erfc(1/2*s)...
% +1/4*s*exp(1/4*s^2)*exp(1/4*s^2)
%
% fhat = (1+t^2)*exp(t^2)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% However,
syms s
fhat2 = ilaplace(1/4*pi^(1/2)*exp(1/4*s^2)*erfc(1/2*s)...
1/8*pi^(1/2)*s^2*exp(1/4*s^2)*erfc(1/2*s)...
+1/4*s*exp(1/4*s^2)*exp(1/4*s^2) )
% Command line Answer
%
% ??? Error using ==> erfc
% X must be real.
I checked the documentation and all of the erf
related function are only defined for real arguments
Hope this helps.
Greg_
