Sol.7.2 - Definition of the Laplace Tbansforrn Definition...

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Unformatted text preview: Definition of the Laplace Tbansforrn Definition and integration by parts twice, we compute 3) "'"'lJ 2t aL cosbt dt l, I/+oo s2 +b2-s'^/ (-s cos bN * b sin bl/) le : lim l- ,_* L s2 +b2-sl I-_.nl s'+ 0" ) s2 +b2', I'HAPTER 7: Laplace Transforms :\ERCISES 7.2: 2. For ,s ) 0, using L {t'z) (s) because, for s-1. For s > 3, we : I "-*r,d,: J11 | "-,'t, at 00 : rim [-tt- t" ' nl I ,-- L " ,J .i I t, "' atf: Jl% (-f - : JT'L t; - (T. '4 *;) "-"'] : 3, > 0 and any k, Ykr-sN -+ 0 as ly' -* oo. have L{ter}{") : I e-,,tes,o,: I1"G s)td,: JgL Iteo-,tt at 000 :Jr*(* -, H"''-""li : lim t l'*( n - 1 )o,r-",r1 : , N--[(3-s)' \3-" (J-t)r/" ] (s-s1z' 6. Referring to the table of integrals on the inside front cover) we see that, for s ) 0, v^[ .C {cos bf } (.s) : | "-"' cosbf dt : lim | ,-"t J N-*.1 uo : ,'r' e-"t (-s cos bf + 6 sin 6f) where we have used integration by parts to find an arrtiderivative of e-'t cos2t....
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This note was uploaded on 03/30/2009 for the course MA diff eq taught by Professor Fenn during the Spring '09 term at N.C. State.

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Sol.7.2 - Definition of the Laplace Tbansforrn Definition...

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