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LAPLACE TR
RANSFORM
Pierre Simon de Laplace (1749 – 1827)

1

INTRODUCT
TION

Laplace Transform is a mathematical t
tool which can be used to solve severa

problems in science and engineering
...


The Laplace Transform finds particul applications in the field of signal
lar

and linear system analysis
...


Pierre Simon de Laplace (1749 – 182 was a French mathematicians and
27)

Astronomer
...

2

DEFINITIO OF LT
ON
Let

be function defined for

, then the integral:-

is said to be a Laplace Transf
form of

provided the integral

convergence
...


5

PIECEWISE CTS FU
UNCTION
A fn

is said to be piecew cts over the interval
wise

if

that interval can be divided into a finite number of
subintervals, say
a
...


s
...


6

EXISTENCE OF LAPLACE
E TRANSFORM

Let

be piecewise cts on the interval [
s

exponential order f f
i l d for for

Then,
Th

and
exist for
i f

7

PROPERTIES OF LAPLAC
CE TRANSFORM
1
...
Shifting property
If

is a function having Laplace Transform

8

EXERCISES
1
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sinht

3
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5
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7
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9
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11
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9



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