# 7.1 Notes - Deﬁnition of the Laplace Transform...

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Unformatted text preview: Deﬁnition of the Laplace Transform Bikerentiai'éniiéiinns’w Section 7.1 Lapinoew’fmnsfofm . Let f be a function deﬁned for (3 0. Then the integral L{f(t)}= fe‘i'ﬂr) dt is said to be the Laplace transform off. provided the integral converges. [7 Exampleéi u . Find L{e"’} using the deﬁnition ofthe Laplace transform. I Find L{r1} using the deﬁnition oftne Laplace transform. M M ii! Notes - When the integral converges. the result is a function of s. - We will use a lowercase letter to denote the function being transformed and the con-esponding capital letter to denote its Laplace tmnsfon'n. For example. Llf<:)}=F(s) and ng(:)}=6(s) l Examﬁles From the Tet“ - Section 7.1 u#6 u#8 l Transforms of Some Bastc Functtons l 5 L1 =— a = {} s L[coskr} 52+? L{r}:31"";T,n=L2,3,K l l H Sufﬁcient Condition for Existence . if a functions is of exponential order the Laplace transform is guaranteed to exist. - However, the Lapiace transform may exist even if the function is not of exponential ...
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## This note was uploaded on 01/13/2012 for the course MATH 2914 taught by Professor Pamelasatterfield during the Fall '10 term at NorthWest Arkansas Community College.

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7.1 Notes - Deﬁnition of the Laplace Transform...

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