Change Of Scale Property _ Laplace Transform _ Advance Engineering Mathematics Review.pdf v1v53

9/3/2018

Change of Scale Property | Laplace Transform | Advance Engineering Mathematics Review

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Change of Scale Property | Laplace Transform

Change of Scale Property If

L {f (t)} = F (s)

, then,

1 L {f (at)} =

s F (

a

) a

Proof of Change of Scale Property ∞ −st

L {f (at)} = ∫

e

f (at) dt

0

Let z = at t = z/a dz dt = a

when

t = 0, z = 0

when

t = ∞, z = ∞

∞ −s(z/a)

L {f (at)} = ∫

e

dz f (z) a

0 ∞

1 L {f (at)} =

−(s/a)z

∫ a

e

f (z) dz

0

Hence, 1 L {f (at)} =

s F (

a

)

okay

a

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Change of Scale Property | Laplace Transform | Advance Engineering Mathematics Review

Tags: Laplace

proof

Laplace transform

change of scale

Problem 01 | Change of Scale Property of Laplace Transform Problem 02 | Change of Scale Property of Laplace Transform Problem 03 | Change of Scale Property of Laplace Transform ‹ Problem 02 | Second Shifting Property of Laplace Transform

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Problem 01 | Change of Scale Property of Laplace Transform › to post comments

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Change of Scale Property | Laplace Transform | Advance Engineering Mathematics Review

Infinite Series Laplace Transform Laplace Transform by Direct Integration Table of Laplace Transforms of Elementary Functions Linearity Property | Laplace Transform First Shifting Property | Laplace Transform Second Shifting Property | Laplace Transform Change of Scale Property | Laplace Transform Problem 01 | Change of Scale Property of Laplace Transform Problem 02 | Change of Scale Property of Laplace Transform Problem 03 | Change of Scale Property of Laplace Transform Multiplication by Power of t | Laplace Transform Division by t | Laplace Transform Laplace Transform of Derivatives Laplace Transform of Intergrals The Inverse Laplace Transform

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