Laplace – The Mathematician

His transformation methods is considered as one of the most effective tool to simplify very complex problems

Born on 23rd March 1749 at Normandy – The Kingdom of France, Pierre-Simon Laplace was a polymath scholar, who contributed in the field of Engineering Mathematics. Laplace was a great scientist of all time- arguably one of the great mathematicians, who is still remembered for his contribution for the development of Engineering mathematical tools, which he summarized in different volumes.

Laplace was also known as a physicist, for his work in the field of mechanics, by predicting the existence of black holes. In statistics he developed the Bayesian interpretation of probability. However, one of the greatest works of Laplace was the development of Laplace Transform, Laplace’s equation, inverse Laplace, Laplacian, Laplace distribution, Laplace number, Laplace limit, Laplace invariant, all these topics are of great importance in Engineering Mathematics - as he formulated these equations and pioneered the transform methods in engineering. According to Wikipedia, "Pierre-Simon Laplace" belongs to a “peasant farming” family. The encyclopedia revealed that his father owned and farmed some small estates, and his uncle was a secondary school teacher and taught mathematics. However, much of the information regarding early life of "Laplace" was lost when the home of his great-great- Grandson, “Comte de Colbert-Laplace”, burned in 1925.

Laplace received his basic education at the "Benedictine priory school", because his father intended that he become a Roman Catholic priest. However, from beginning "Laplace" was in love with numbers, as he entered “Caen University” in 1765 to study theology, while there he discovered his passion and show-off his Mathematical talent at the "University of Caen" and wrote "Calculus" by using Laplace transform method, after which the two professors of the Caen University "C. Gadbled and P. Lecanu" from the Department of Mathematics, realized his mathematical potential. Later "Laplace" left for Paris and began to study Mathematics. After that Laplace found a position for his contribution as a Professor and started his career as an academician, after that he had written remarkable series of Mathematic research papers. His first publication was on “Maxima” and “Minima” of curves and afterwards he produced the paper on differential equations. His first paper on “Integral calculus” appeared in the print which he has translated into Latin- published at Leipzig in the Nova acta eruditorum.

Laplace also examined some mathematical applications of astronomy, like on the inclination of planetary orbits- a study of how planets were perturbed by the moon. Besides some study on the stability of solar bodies, by using Newtonian Physics and Euler’s earlier research, Laplace concluded that any two planets and the sun must be in equilibrium for the solar system to remain stable. Besides he introduced spherical harmonics and the concept of gravitational potential in celestial mechanics. Laplace developed the concept of scalar potential to define how gravitational vectors behave. His nebular hypothesis is currently adopted for the explanation of planetary origins. The "Laplacian operator" introduced by him is still of great importance in higher studies curriculum, which is sill used in physics to perform the mathematical operation, related to vector physics. If we have a multivariable function like (F), and take it into two-dimensional input, then it gives us f (x1y) and the "Laplacian" (f) gives a new scalar valued function of X and Y with second derivative, because the way it is defined is that, we take the divergence of the gradient of the function (f), which is vector physics operation, by using "Laplace transform method".

Laplace mathematical style has consistently gained reputation as well a philosophical position. He is still remembered on his contribution of solving “Differential equations” by taking various parameters and steps using his "Laplace & inverse laplace" method, widely used by electrical & electronic engineering students, to quickly solve differential equations occurring in the analysis of electronic circuits, communication engineering, control system engineering, digital signal processing, system modelling and Nuclear physics, besides various applications in science & engineering, that is why it is used as an integral transform in mathematics.

Laplace’s deep study resulted in a number of quantitative methods in mathematics and physics, which made him one of the influential scientists. His contribution is widely considered across the globe, due to his wide knowledge and caliber as he dominated all discussions in Mathematical sciences. His transformation methods is considered as one of the most effective tool to simplify very complex problems in the area of stability & control. On 5th of March 1827 Laplace died and “The French Academy of sciences” marked this day as a tribute to this influential Mathematician

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