laplace-table - S. Boyd EE102 Table of Laplace Transforms...

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S. Boyd EE102 Table of Laplace Transforms Remember that we consider all functions (signals) as deFned only on t 0. General f ( t ) F ( s ) = Z 0 f ( t ) e - st dt f + g F + G αf ( α R ) αF df dt sF ( s ) - f (0) d k f dt k s k F ( s ) - s k - 1 f (0) - s k - 2 df dt (0) -···- d k - 1 f dt k - 1 (0) g ( t ) = Z t 0 f ( τ ) G ( s ) = F ( s ) s f ( αt ), α > 0 1 α F ( s/α ) e at f ( t ) F ( s - a ) tf ( t ) - dF ds t k f ( t ) ( - 1) k d k F ( s ) ds k f ( t ) t Z s F ( s ) ds g ( t ) = ( 0 0 t < T f ( t - T ) t T , T 0 G ( s ) = e - sT F ( s ) 1
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Specifc 1 1 s δ 1 δ ( k ) s k t 1 s 2 t k k ! , k 0 1 s k +1 e at 1 s - a cos ωt s s 2 + ω 2 = 1 / 2 s - + 1 / 2 s + sin ωt ω s 2 + ω 2 = 1 / 2 j s - - 1 / 2 j s + cos( ωt + φ ) s cos φ - ω sin φ s 2 + ω 2 e - at cos ωt s + a ( s + a ) 2 + ω 2 e - at sin ωt ω ( s + a ) 2 + ω 2 2
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Notes on the derivative formula at t = 0 The formula L ( f 0 ) = sF ( s ) - f (0 - ) must be interpreted very carefully when f
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This note was uploaded on 09/28/2009 for the course X RAY MECH EMP5209 taught by Professor Hui-leo-chen during the Fall '09 term at University of Ottawa.

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laplace-table - S. Boyd EE102 Table of Laplace Transforms...

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