Laplace Transform - How was it created?

[Vargas]

The well know Laplace Transform, that is :

int (e^(st)f(t)) dt
0->00

was really reated by Laplace or other person ?

And how he concluded that ?

 

[HallsofIvy]

Yes, the Laplace transform was really developed by Laplace. As for how "how he concluded that ?", concluded what?

 

[Vargas]

More about Laplace

Dear friend,
The problem started qhen I read this:
Laplace Transform
Thu, 4 Jul 1996 00:45:29 -0400
Julio Gonzalez Cabillon
At Wed, 26 Jun 1996 00:49:25 -0400 Sherman Stein asked:

Did Laplace invent the Laplace transform? Why? I mean "what ma-de him think of it?" Is there a historical introduction to it and similar
transforms?
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and at Thu, 27 Jun 1996 21:12:57 -0400 Mike Deakin answered:
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Laplace did not invent the Laplace Transform; Euler did.

This seems very impressive to me!
When did Euler introduce -I dislike the word "invent"- what we now call the *Laplace Transform*? Where exactly? I mean... in which of his papers? Are you thinking of Euler 1736-37 books and papers, specially 1737? Obviously, Euler did not "invent" -as you say- the standard modern version of the Laplace Transform. So?...
Do I understand rightly from your answer that you are ignoring or failing to recognize Laplace contribution to the topic?

Moreover Laplace said so (though he got the reference wrong).

When and where exactly Laplace said so? Which was his mistaken reference?

Later it was rediscovered by the lesser-known mathematician Jo-sef Petzval, who wrote a 2-volume tome on it. Petzval fell out with one of his students, Simon Spitzer, who took his revenge by promulgating the myth that his teacher had plagiarised Laplace (e-ven after Euler's priority had been pointed out to him!).

The name stuck

Are you intending to say that because of a student of Petzval we today
ascribe to Laplace this transform?

>because Boole and later Poincare read and accepted Spitzer's assertion. Initially Poincare attributed the transform to Bessel (presumably because he misheard the name "Petzval").

Who is presuming that confusion? And as you said "Initially Poincare
attributed..." I would like to know who attributed to Laplace the Transform in the long run?... Poincare?...

>All this history relates to an earlier (and in some ways bet-ter) form
of the transform in which a generalised *inverse* transform was used.
It was indeed Poincare who first got this off the ground prop-erly (the earlier researchers did'nt know enough complex analy-sis). Poincare 1st announced his discovery in a still unpublished paper -- Part I of "Non Inultus Premor", his submission (which didn't win) for the Academie's "grand prize" of 1880.
I read this in 1980 (when there was some hope that it would appear) in
difficult circumstances, This seems chinese to me... What do you want to express with "difficult
circumstances"?

Sorry about the questions!... But your answer without concrete references -specially to crucial points- does not help to clarify much. If one reads the query and your reply, Laplace seems to ap-pear in connection with the so-called LT almost by chance. And pe-rhaps *chance* or better *probability* has much to do with what made him think of LT (in its primitive form).

Thanks in advance.
Prof. Julio Gonzalez Cabillon
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I think that it's a very interested question, don't you think so ?
And about my question, "Conclude", you're right. My English it's really bad.
It was mean : " How understood Laplace that those integral applied on differential equations could simplified them"? And what means S-Domain ?