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+--- Thread: laplace confusion.... (/thread-8659.html)
laplace confusion.... - webmasterpdx - 07-10-2017 02:38 AM
Normally when we do a laplace transform, we use a function of the form f(t), a function of t, time, and the result should be a function of s, F(s), but in the example given in the user manual, they use a function of x....
e.g. If f(t) = e^(a*t), so if I try laplace(e^(a*t)), I get (e^(a*t))/x, which is wrong....should be F(s) = 1/(s-a).
So, I decided to use x instead since the user guide example used x....so I used:
laplace(e^(a*x)) gave a result of F(x) = 1/(x-a)
So, am I correct in assuming that we should use x instead of t when defining f(t), and in the result from the laplace() function, we should assume again that x is really s in the results also.....
....as in the latter example, I converted f(t) to f(x) as in...
f(t) = e^(a*t) -> f(x) = e^(a*x)
....and likewise, in the result, we get F(x) = 1/(x-a) and converting to s, we get...
F(s) = 1/(s-a)
....which is the correct answer.
So, am I correct then, in assuming that we should always convert f(t) to f(x) before calling laplace() and convert our results from F(x) to F(s)???????????
Thx
-Donald
RE: laplace confusion.... - Thomas_Sch - 07-10-2017 05:30 AM
regarding https://www-fourier.ujf-grenoble.fr/~parisse/giac/cascmd_en.pdf (page 322)
"... Or input : laplace(sin(t),t)
here the variable name is t and this name is also used in the answer.
Output : 1/((-t)^2+1)
Or input : laplace(sin(t),t,s)
here the variable name is t and the variable name of the answer is s.
Output: 1/((-s)^2+1) "
you could enter: laplace(e^(a*t),t,s)
and get what you want.
RE: laplace confusion.... - webmasterpdx - 07-10-2017 10:01 AM
Ah, OK, undocumented was the problem. Is laplace(f(t), t, s) to get conventional function values using appropriate variables. So, my example of laplace(e^(a*t),t,s) gives me the correct result of -1/(a-s), which is 1/(s-a).
So, someone needs to add the 2 arguments to the documentation.
Thanks
-Donald
RE: laplace confusion.... - Thomas_Sch - 07-10-2017 02:56 PM
There is an example in the online help for the laplace function.
(Enter "laplace" then press the Help button)