1

• Consider a given function F(s), is it possible to

find a function f(t) defined on [0, ), such that

• If this is possible, we say f(t) is the inverse

Laplace transform of F(s), and we write

Inverse Laplace Transform

? )()}({ sFtfL

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2

• First we note that the Inverse Laplace

Transform is a “ Linear Operator”.

Some Examples.

,

ss

s

. F(s)

,

b(s-a)

b

. F(s)

,

b(s-a)

s-a

. F(s)

102

23

3

2

1

2

22

22

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3

• Consider the Initial Value Problem:

• We shall use Laplace Transform and Inverse

Laplace Transform to solve this I.V.P.

Applications

.12)0(' ,2)0(

;85'2"

yy

eyyy t

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4

• Given the following I.V.P: (#36, P. 406)

Next let us consider a D.E. with

variable coefficents

. 1)0('

2)0(

2'"

y

y

ytyty

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##### Document information

Uploaded by:
sarangapani

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University:
Fakir Mohan University, Balasore

Subject:
Signals and Systems Theory

Upload date:
17/07/2012