The document provides an overview of topics related to the Laplace transform and its applications. It defines the Laplace transform, discusses properties like linearity and examples of transforms of elementary functions. It also covers the inverse Laplace transform, differentiation and integration of transforms, evaluation of integrals using transforms, and applications to differential equations.

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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4. Linearity of the Laplace Transform
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5. Laplace Transform of some Elementary
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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
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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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28. Dirac Delta function
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