required help regarding laplace transform!

ravaila · #1 Friday, May 28, 2010

how L{delta(t)}=1
what is t-shift theorem in laplace n wt is its proof?
what is linearity property in laplace transform?

Bright · #2 Sunday, May 30, 2010

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.

Ayesha Mahmood · #3 Thursday, June 03, 2010

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.

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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) }