Lecture 22 - The Laplace Transform and Initial Value...

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The Laplace Transform and Initial Value Problems Constant Coefficients

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MATLAB Quiz Thursday, March 13 Same Time As Your Section (APM B432) DON’T FORGET!!!! (NO MAKEUPS)
Friday… L { f ( t ) } ( s ) f ( t ) dt = e - s t Z 1 0 We Introduced the Laplace Transform “Transforms” Independent Variable For Example L e a t = 1 s - a

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Inverting The Laplace Transform Can Go Backwards: L e a t = 1 s - a L { y } = 1 s - 3 y = e 3 t Known as “Inverting the Laplace Transform” There’s a Big Table of Known Laplace Transforms In The Book
Laplace Transforms of Derivatives BIG IDEA: The Laplace Transform “Transforms” Derivatives In A Special Way L { y 0 } = dt e - s t Z 1 0 y 0 Integration By Parts = e - s t Z 1 0 - s y dt e - s t y 1 0 ! Assume: < e D t For Some D = 0 y (0) + s L { y } - - | y |

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Laplace Transforms of Derivatives BIG IDEA: The Laplace Transform “Transforms” Derivatives In A Special Way L { y 0 } = Assume: < e D t For Some D y (0) - s L { y } No Derivatives! | y |
Laplace Transforms of Derivatives BIG IDEA: The Laplace Transform “Transforms” Derivatives In A Special Way L { y 0 } = Assume: < e

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