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#1
Friday, May 28, 2010
 Senior Member Join Date: Jan 2008 Location: city of miTTi kaTTA Posts: 922 Thanks: 1,565 Thanked 778 Times in 431 Posts
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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#2
Sunday, May 30, 2010
 Member Join Date: Feb 2010 Location: Islamabad Posts: 78 Thanks: 0 Thanked 38 Times in 29 Posts

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.
 The Following User Says Thank You to Bright For This Useful Post: ravaila (Sunday, May 30, 2010)
#3
Thursday, June 03, 2010
 Senior Member Join Date: Jan 2010 Location: DGKhan & Isb Posts: 383 Thanks: 391 Thanked 256 Times in 180 Posts

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) }
 The Following User Says Thank You to Ayesha Mahmood For This Useful Post: ravaila (Thursday, June 03, 2010)