Laplace transform and its applications

1. Made By:-
S.Y. M-2
Shah Nisarg (130410119098)
Shah Kushal(130410119094)
Shah Maulin(130410119095)
Shah Meet(130410119096)
Shah Mirang(130410119097)
Laplace Transform And Its
Applications

2. 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

3. 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.
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0
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4. Linearity of the Laplace Transform
 If L{f(t)}= and then for any
constants a and b
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11. Inverse Laplace Transform
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13. Laplace Transform of Derivatives &
Integral
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15. Differentiation & Integration of Laplace
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18. Evaluation of Integrals By Laplace
Transform
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19. Convolution Theorem
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21. Application to Differential Equations
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23. Laplace Transform of Periodic Functions
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25. Unit Step Function
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26. Second Shifting Theorem
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28. Dirac Delta function
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