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Lecture 20
Into.to
LaplaceTransforms
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Laplace Trusts• piecewise continuous For some M, a , and K,
+It) :. subexponential growtht fitness:f:i." " "↳
subexponentialgrowthtxamples.
-
L { D= ?
L feat} s ?
L{ caslbtt}s?
L{ sinlbtl } ' ?
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tapeworms• Heat :[eat-stat
Angie, :( piecewise antinous =fgizf"e'"'a'tat
• doesn't grantor^ sat =¥n. H
5-HI✓ for s > a.¥ so
g{eat3'If#Is meat fort > KThen
,the Laplacetransform
i:÷÷÷¥÷:¥÷i÷÷÷÷÷÷:i÷÷÷:*.in.tianya.slo.se-stat =¥m."A)t÷s= 's.is
sting, fttettdt bassos.
=aliggfgsh) - ='s = statist
÷: so :i:"÷÷
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Linearity
④L{afHtbgHB=aL{fHYtbLfgk#
• Derivatives :
④ Ll5HB=sL¥Lfsikf-SLHHI-sfld.si
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5.dvingInitialValuePnoblemsusingLaplacetransforna y"t by't Cy s Elt) * LEH=sLH*{ gloss yo y'lo) s yo' *
[email protected]"- 3g'
+2g so④ LlsH=sL¥{ gloss 2 y'lol : 't Lfstal-ILHHI-sfld.si
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• Applicationto initial value problem :
•Derivatives:
ayxtbjtcg.tk#Lfsttis=sLffkt-flD{ 2g%dg;
prog fo%ae-stdt-l.gg '
HE"dtLet ftp.LHHH
Integrateby parts) . 161=212411=algin fittest]! -fffktf.se#ThmafsI4sl-syo-giItbfst4sl-ydtcI4l= - flat fototttlestdt = FCS)
= LISH} - flo)OtohforIts. Lls sina.ss.io, .jo, tests tudou.IT#tbI
It : the #time aofdeaos :So Htt Lifted)
21*1=21*13 .Combing : we can she
sL{FAB-shotthe IVP if
=s{sL{ftp.floy-ggg.q are
① we can amputee =L{fHf
② We can compute L"IICD) .
.