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Inverse Laplace Transforms

# Inverse Laplace Transforms - Differential Equations Second...

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Differential Equations Second Quarter SY 0506 ____________________________________________________________________________________________________________ Silva, Alviso and Llacuna – Mathematics Department, MIT 167 Lesson 33 Inverse Laplace Transforms Specific Objectives: At the end of the lesson, the students are expected to: define Inverse Laplace Transform find the inverse Laplace transforms of a function Note: The Table of Laplace transform can be used to find the inverse Laplace transforms If ( ) F s represents the Laplace transform of a function ( ) f t , that is, ( ) { } ( ) L f t F s = then ( ) f t is the inverse Laplace transform of ( ) F s , that is, ( ) { } 1 L F s . { } ) ( ) ( 1 t f s F L = Table of Inverse Laplace Transform 1. 1 1 1 L s = 2. ( ) 1 1 at L e s a = 3. ( ) 1 1 1 , 1,2,3,... 1 ! n n t L n s n = = 4. ( ) ( ) 1 1 1 1 ! n at n t L e n s a = 5. 1 1 ! n n n L t s + = 6. 1 2 2 sin k L kt s k = + 7. 1 2 2 cos s L kt s k = + 8. 1 2 2 sinh k L kt s k = 9.

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