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Kiarash Rahbar (Student I.D. 1203691159)MAT 275Honors ProjectThe Father of the Laplace TransformThe creation of Laplace’s equation and the Laplace transform has been beneficial to a wide range of applications within physics and engineering as a whole. The creation of this integral transform can be credited to the French mathematician and astronomer, Pierre-Simon Laplace, whose work has been a detrimental addition to the developments in mathematical astronomy and statistics. Laplace has been remembered as one of the best scientists of all time and is sometimes even referred to as the “French Newton”. The explanations of his work and the extended work of others were published in the five-volume Mécanique Céleste. The work found in this publishing translated classical mechanics, which was of geometric study, into one based on calculus. This was beneficial to the field of physics because it opened up a broader range of problems. Laplace was also a huge inventor within the field of statistics in which he developed the Bayesian interpretation, which is a subset of evidential probabilities. Laplace’s influence on France was so detrimental that he became a count of the First French Empire in 1806 and in 1817 was named a marquis.Most of the information on Laplace’s life had been lost with the burning of his family house in 1925. However it is known from reliable sources that Laplace was born in Normandy in 1749 and was the son of a small cottager or farm-laborer. At age sixteen, Laplace was sent to the University of Caen to read theology. It was here that Laplace was introduced to the idea of mathematics by two teachers who ended up guiding him to leave for Paris with a letter of introduction to Jean le Rond d’Alembert. There are many stories as to the interactions between d’Alembert and Laplace, however most end in Laplace gaining d’Alembert’s respect by proving his incredible skill for mathematics. He then secured a teaching place in Ecole Millitaire with a recommendation from d’Alembert. For the next 17 years of his teaching, Laplace became engulfed with original research and produced most of his original work in astronomy. At age 24, he was elected associate member to the Academie. By the time he was 39, Laplace had married the 18 year old Marie-Charlotte de Courty de Romanges. The couple had two children together, a son and a daughter.Around the year 1744 noted mathematicians Euler and Lagrange had started to look for solutions of differential equations in the form z= X(x)eαxdx and = XxxAdx EQ . However, in 1785, Laplace took a detrimental step forward by using the integrals of these specific forms to transform a whole difference equation as opposed to just finding a form for the solution. He found that by doing this, the transformed equation was easier to solve than the original. Laplace had soon come to recognize that Joseph Fourier’s method of Fourier series that solved diffusion equations could only be applied to a limited area of space because the solutions were periodic. However, Laplace was able to apply his transform in 1809 to find solutions that diffused indefinitely in space. The use of the transform became popular shortly following World War II, however noted mathematicians such as Abel, Lerch, Heaviside and Bromwich had used it seldom in the 19th century. The Laplace transform can also be used in pure and applied probability in which it is defined as an expected value. This gives one the ability to find the probability distribution of a random variable from the Laplace transform. The Laplace transform also has applications within probability theory and has been seen in Markov chains as well as renewal theory, which are first passage times of stochastic processes. The Laplace transform was just one of the many contributions Laplace had given to the fields of mathematics and astronomy. Other discoveries of Laplace include the proof that every equation of an even degree must have one real quadratic factor, a solution of the linear partial differential equation of the second order as well as the discussion of the general theory of determinants which was in parallel with Alexandre-Theophile Vandermonde. Although he was born a catholic, Laplace spent most of his life changing between deism and atheism. Throughout his old age, he remained curious about the existence of God and frequently discussed Christianity with fellow astronomers. However, it is believed he remained agnostic in his final years. Laplace’s life came to an end in Paris in 1827. His brain was removed and kept for many years to eventually be displayed in a roving anatomical museum in Britain who reported that it was smaller than the average brain. ................
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