Laplace_Transforms

# Laplace_Transforms - TABLE OF LAPLACE TRANSFORMS Revision I...

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1 TABLE OF LAPLACE TRANSFORMS Revision I By Tom Irvine Email: [email protected] April 27, 2011 Operation Transforms N F(s) f (t) , t > 0 1.1 0 dt ) t ( y ) st exp( ) s ( Y y(t) , definition of Laplace transform 1.2 Y(s) j c j c ds ) s ( Y ) st exp( 2 j 1 ) t ( y inversion formula 1.3 sY s y 0 y (t) , first derivative 1.4   ) 0 ( y ) 0 ( sy s Y 2 s ) t ( y , second derivative 1.5   )] 0 ( ) 1 n ( y [ )] 0 ( ) 2 n ( y [ s )] 0 ( y [ 2 n s )] 0 ( y [ 1 n s s Y n s ) t ( ) n ( y , nth derivative 1.6   s F s 1 t 0 , d ) ( Y integration 1.7 F(s)G(s) t 0 , d ) ( g ) t ( f convolution integral 1.8 s F 1 f( t), scaling 1.9 F(s - ) exp( t) f(t), shifting in the s plane 1.10 s F 1   ) t ( f t exp  , combined scaling and shifting

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2 Function Transforms N F(s) f (t) , t > 0 2.1 1  t , unit impulse at t = 0 2.2 s ) t ( dt d , doublet impulse at t = 0 2.3 exp(- s    ) t ( 2.4 s 1 u(t) , unit step 2.5 ) s exp( s 1 ) t ( u 2.6 2 s 1 t 2.7 .... , 3 , 2 , 1 n , n s 1 )! 1 n ( t 1 n 2.8 .... , 3
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Laplace_Transforms - TABLE OF LAPLACE TRANSFORMS Revision I...

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