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laplace-table

# laplace-table - Laplace Transform of discontinuous...

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In everything below we assume that f ( t ) is piecewise continuous on [0 , ) and of exponential order and F ( s ) is its Laplace Transform Laplace Transform F ( s ) = Z 0 e - st f ( t ) dt Table of Laplace Transforms f ( t ) F ( s ) 1 1 s e at 1 s - a cos bt s s 2 + b 2 sin bt b s 2 + b 2 e at cos bt s - a ( s - a ) 2 + b 2 e at sin bt b ( s - a ) 2 + b 2 t n n ! s n +1 e at t n n ! ( s - a ) n +1 e at f ( t ) F ( s - a ) f 0 ( t ) sF ( s ) - f (0) f 00 ( t ) s 2 F ( s ) - sf (0) - f 0 (0) t n f ( t ) ( - 1) n d n F ds n ( s ) Laplace Transform in the limit lim s →∞
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Unformatted text preview: Laplace Transform of discontinuous functions L{ f ( t ) u ( t-a ) } ( s ) = e-as L{ f ( t + a ) } ( s ) L-1 { e-as F ( s ) } ( t ) = f ( t-a ) u ( t-a ) Laplace Transform of periodic functions F ( s ) = 1 1-e-sT Z T e-st f ( t ) dt...
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