Notes on The Convolution Integral - Differential Equations Transforms | MATH 267, Study notes of Mathematics

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The Conarolutvon Intes ral To Solwé@ an intial tra lue Prob lem we often neect to | Innere the Product of tudo Laplace tan fForms, FCS)+ (6s), Theorem: TF FesheLiFearp, Gesy=L {oe} beth exise For S>220° then Hes) = Fes) Gesy= Li heed}, Where + re het) = f Flee) gcey de = [rerrge-vode. Ts theoreen Says thet » Prowided we Con invere Fes) £ Gee) indinri dually to Find £04) g git), we Can inwere the Product FCS): 6¢s) by Computing the Conia lutisn tates re/ S* Fee-ed 90x) dt= J scegu-) AT the Cpuslity oF these two integrals Folens by the Change os MWariable VW=t-T ; Be -AT.