lets start a riot!! :)
this is what ive written so far
The search on Laplace has portrayed him as a rather arrogant, egotistical, narcissist. Yet, it appears that he had the wherewithal to back up such an attitude. Laplace created many new mathematical methods, but his motivation with regards towards mathematics rested in its capacity to help him study nature. In his acclaimed work, Traite de Mechanique Celeste, Laplace used calculus and differential equations, along with Newton’s theories pertaining to gravity and celestial motions, to solve many of the issues that had been left open by the emerging theories of his day. Laplace is known for his founding work in probability theory as well. His book entitled, Theorie Analytique des Probabilites, includes some basic applications of what we today refer to as the Laplace transform. The Laplace transform is one of the oldest integral transforms that have been used in finding solutions to linear differential equations and integral equations. Euler is actually credited with introducing integral transforms; but, it was Spitzer who attached the name “Laplace” to the expression: y=abesx fs ds. When used appropriately, the Laplace transform reduces the problem of finding a solution to a differential equation by literally transforming the diffyQ into an algebraic expression. Today, the Laplace transform usually takes a form similar to:
F(s)=L(f(t))= int[0,∞) e-st f(t)dt
With some restrictions to the values that we can use for s this structure transforms f(t) into a function of s. The Laplace transform has the attribute that it creates a unique solution that can be inverted to obtain a suitable solution to the given equations.