Application of Laplace Transforme

Laplace Transform And Its
Applications
Subject: Advanced Engineering Mathematics(2130002)
Branch: Civil Engineering (3rd Sem.)
Guided by:-
Dr. Manisha Patel

Name Enrollment No.
Maharshi Dave 160420106007
Kishan Bhanderi 160420106022
Nimesh Nakrani 160420106032
Smit Savaliya 160420106057
Namat Uttah 160420106067
Deep Kalthiya 1604201060
Team Members:-

Topics
 Definition of Laplace Transform
 Linearity of the Laplace Transform
 Laplace Transform of some Elementary Functions
 First Shifting Theorem
 Inverse Laplace Transform
 Laplace Transform of Derivatives & Integral
 Differentiation & Integration of Laplace Transform
 Evaluation of Integrals By Laplace Transform
 Convolution Theorem
 Application to Differential Equations
 Laplace Transform of Periodic Functions
 Unit Step Function
 Second Shifting Theorem
 Dirac Delta Function

Definition of Laplace Transform
 Let f(t) be a given function of t defined for all
then the Laplace Transform ot f(t) denoted by L{f(t)}
or or F(s) or is defined as
provided the integral exists,where s is a parameter real
or complex.
0t
)(sf )(s
dttfessFsftfL st
)()()()()}({
0



 

Linearity of the Laplace Transform
 If L{f(t)}= and then for any
constants a and b
)(sf )()]([ sgtgL 
)]([)]([)]()([ tgbLtfaLtbgtafL 
)]([)]([)}()({
)()(
)]()([)}()({
Definition-By:Proof
00
0
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dttbgtafetbgtafL
stst
st
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
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




Laplace Transform of some Elementary
Functions
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Laplace Transform of Derivatives &
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f(0)-(s)fsf(0)-sL{f(t)}(t)}fL{
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Differentiation & Integration of Laplace
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Laplace Transform of Periodic Functions
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Unit Step Function
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Second Shifting Theorem
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Dirac Delta function
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

Application of Laplace Transforme

Application of Laplace Transforme

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