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#1
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required help regarding laplace transform!
how L{delta(t)}=1
what is t-shift theorem in laplace n wt is its proof? what is linearity property in laplace transform? |
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umer shakeel (Friday, July 24, 2015) |
#2
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Ravaila i didn't remember proof such transformation 2004 ma para tha. ab to chor diya ha. i think u must consult Mathematical Method of B.Sc of Punjab University under laplace transformation u\ll found ur require result inshallah.
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ravaila (Sunday, May 30, 2010) |
#3
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Shift Theorem Or the First Transform theorem:
Statement: If F(s) is the Laplace Transform of f(t), then F(s-a) is the Laplace transform of exp(at).f(t) . Proof: (integral limit is from 0 to infinity) L{ e^(at) . f(t) } = integ { e^ (-st) e^ (at) f(t) dt } = integ { e^( - (s-a)t ) f(t) dt } put s-a=s', so that L { e^ (at) . f(t) } = integ { e^ (-s' t) f(t) dt } = F(s' ) = F(s-a) this completes the proof. ------------------------------------------------------------- Laplace Transform is a Linear Operator:( Linearity Property Of Laplace Transform) L { a f(t) + b g(t) } = a L { f(t) } + b L { g(t) } |
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ravaila (Thursday, June 03, 2010) |
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