ABSTRACT
One of the oldest and most commonly used linear integral transformations is the Laplace transformation. It dates back to the work of the French mathematician, Pierre Simon Marquis de Laplace (1749-1827), who used it in his work on probability theory in the https://www.w3.org/1998/Math/MathML"> 1780 s https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138752859/46b98bf4-f43d-4c1b-bad9-d831e2ef6414/content/eq2406.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . His major work [136] Théorie analytique des probabilités of 1812 also contains some of his results on this integral transformation. Although the Laplace transformation was also cited in Fourier's famous paper [66] on heat conduction in 1811, it was the English electrical engineer Oliver Heaviside (1850-1925) who made it popular by using it to solve elementary ordinary differential equations and to develop the operational calculus https://www.w3.org/1998/Math/MathML"> [ 98,99 ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138752859/46b98bf4-f43d-4c1b-bad9-d831e2ef6414/content/eq2407.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> .
