Presentation on theme: "Pierre-Simon Laplace. Content Life of Laplace Carrier Articles Laplace Transform Inverse Laplace Transform Basic Laplace Transform Pairs Z- Transform."— Presentation transcript:
Content Life of Laplace Carrier Articles Laplace Transform Inverse Laplace Transform Basic Laplace Transform Pairs Z- Transform
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)
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)
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
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.
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
Inverse Laplace Transform Various name for inverse laplace transform – Bromwich integral – Fourier-Mellin integral – Mellin’s inverse formula y is a real number
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
What we know is not much. What we do not know is immense.
References 11/pierre-de-laplace-hayat-ve-olaslklar.html 11/pierre-de-laplace-hayat-ve-olaslklar.html laplace-kimdir-laplace-nin-hayati-ve- basarilari/ laplace-kimdir-laplace-nin-hayati-ve- basarilari/ Simon_Laplace Simon_Laplace m m