He formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him.
He restated and developed the nebular hypothesis of the origin of the solar system and was one of the first scientists to postulate the existence of black holes and the notion of gravitational collapse.
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Laplace will only generate an exact answer if initial conditions are provided
laplace of sin(at) = (a ) / (s^2 + a^2) thus, laplace of sin 23t, just fill in for a=23 (23) / (s^2 + 23^2) thats it...
The Laplace equation is used commonly in two situations. It is used to find fluid flow and in calculating electrostatics.
Pierre de fermat developed the number theory but was not found true until someone discovered and took place as the founder.
the Laplace transform of sin2 3thttp://www7.0zz0.com/2009/12/30/19/748450027.gif