Laplace transforms Definition of Laplace Transform First Shifting Theorem Inverse Laplace Transform Convolution Theorem Application to Differential Equations Laplace Transform of Periodic Functions Unit Step Function Second Shifting Theorem Dirac Delta Function

1. GUJARAT
TECHNOLOGICAL
UNIVERSITY
Subject : Advanced
Engineering Mathematics
Sem-3 (Chemical)
Topic : Laplace Transforms

2. Topics
 Definition of Laplace Transform
 Linearity of the Laplace Transform
 Laplace Transform of some Elementary Functions
 First Shifting Theorem
 Inverse Laplace Transform
 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 of 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



 

4. Linearity of the Laplace Transform
 If L{f(t)}= and then for any
constants a and b
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)]([)]([)}()({
)()(
)]()([)}()({
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00
0
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


5. Laplace Transform of some Elementary
Functions
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9. First Shifting Theorem
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11. Inverse Laplace Transform
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12. Differentiation & Integration of Laplace
Transform
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13. 3
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14. 
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15. Evaluation of Integrals By Laplace
Transform
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16. Convolution Theorem
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17.  
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18. Laplace Transform of Periodic Functions
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19. 
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20. Unit Step Function
s
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21. Second Shifting Theorem
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