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Pierre-Simon Laplace

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Content Life of Laplace Carrier Articles Laplace Transform Inverse Laplace Transform Basic Laplace Transform Pairs Z- Transform

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Life of Laplace French mathematician and astronomer 23 March 1749 – 5 March 1827 Support of neighbors for education Contact with D’Alembert Supporting young mathematicians (Biot)

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Carrier Studying on theorems of Lagrange, Leipzig – Lagrange:Theoretical mathematic – Laplace: Physics and mathematics Book: “Théorie Analytique des Probabilités” Elected to acedemy Ministry of the Interior(to beat Newton)

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Articles Wrote 13 scientific articles – Implementation of integral calculation to differential equations – Implementation to games of chance – Calculation of integrals in undefined points – Geometry and astronomy First article: Recherces sur les maxima et minima des lignes courbes – New perspective to Euler’s boundary value problems

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Laplace Transform Related to fourier transform Solving differential and integral equations – Fourier transform: express a function as a series of frequencies – Laplace transform: resolves a function into its moments.

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Laplace Transform Used integral transform with many applications in physics and engineering – Electric circuits – Harmonic oscillators – Optical devices – Mechanical systems s is a complex number

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Inverse Laplace Transform Various name for inverse laplace transform – Bromwich integral – Fourier-Mellin integral – Mellin’s inverse formula y is a real number

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Z-transform Simply the Laplace transform of an ideally sampled signal with the substitution of where T = 1/f s is the sampling period and f s is the sampling rate The Laplace transform of the sampled signal is with the substitution of z → e sT we have z-transform

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What we know is not much. What we do not know is immense.

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References http://www.thesecondmessengers.com/2011/ 11/pierre-de-laplace-hayat-ve-olaslklar.html http://www.thesecondmessengers.com/2011/ 11/pierre-de-laplace-hayat-ve-olaslklar.html http://soruvecevap.blogcu.com/pierre-simon- laplace-kimdir-laplace-nin-hayati-ve- basarilari/12930952 http://soruvecevap.blogcu.com/pierre-simon- laplace-kimdir-laplace-nin-hayati-ve- basarilari/12930952 http://tr.wikipedia.org/wiki/Pierre- Simon_Laplace http://tr.wikipedia.org/wiki/Pierre- Simon_Laplace http://en.wikipedia.org/wiki/Laplace_transfor m http://en.wikipedia.org/wiki/Laplace_transfor m

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بسم الله الرحمن الرحيم University of Khartoum Department of Electrical and Electronic Engineering Third Year – 2015 Dr. Iman AbuelMaaly Abdelrahman www.uofk.edu.

بسم الله الرحمن الرحيم University of Khartoum Department of Electrical and Electronic Engineering Third Year – 2015 Dr. Iman AbuelMaaly Abdelrahman www.uofk.edu.

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