# Formulas-1 - 1 Formulas f t F s = L f t t n n/s n 1 n = 0 1 2 and s> e at 1 s a s> a sin kt k s 2 k 2 s> cos kt s s 2 k 2 s> sinh kt k s 2

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Unformatted text preview: 1 Formulas f ( t ) F ( s ) = L{ f ( t ) } t n n ! /s n +1 ; n = 0 , 1 , 2 ,... and s > e at 1 / ( s- a ) ; s > a sin( kt ) k/ ( s 2 + k 2 ) ; s > cos( kt ) s/ ( s 2 + k 2 ) ; s > sinh( kt ) k/ ( s 2- k 2 ) ; s > k cosh( kt ) s/ ( s 2- k 2 ) ; s > k δ ( t- a ) e- as ; s > u ( t- a ) e- as s ; s > L{ f ( t ) } ( s ) = Z ∞ e- st f ( t ) dt L{ e at f ( t ) } = F ( s- a ) L{ u ( t- a ) f ( t- a ) } = e- as F ( s ) L{ t n f ( t ) } = (- 1) n d n ds n F ( s ) L Z t f ( x ) dx = 1 s F ( s ) L ( f ( t ) t ) = Z ∞ s F ( x ) dx L ( d n dt n f ( t ) ) = s n F ( s )- s n- 1 f (0)- s n- 2 f (0)- ...- f ( n- 1) (0) ( f * g )( t ) = Z t f ( x ) g ( t- x ) dx L{ ( f * g )( t ) } = F ( s ) G ( s ) p 1 ( x ) = f + ( x- x ) f [ x , x 1 ] p 2 ( x ) = f + ( x- x ) f [ x , x 1 ] + ( x- x )( x- x 1 ) f [ x , x 1 , x 2 ] p 3 ( x ) = f + ( x- x ) f [ x , x 1 ] + ( x- x )( x- x 1 ) f [ x , x 1 , x 2 ] + ( x- x )( x- x 1 )( x- x 2 ) f [ x , x 1 , x 2 , x 3 ] ....
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## This note was uploaded on 08/24/2011 for the course ENGINEERIN 1122 taught by Professor Stadnik during the Spring '11 term at University of Ottawa.

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Formulas-1 - 1 Formulas f t F s = L f t t n n/s n 1 n = 0 1 2 and s> e at 1 s a s> a sin kt k s 2 k 2 s> cos kt s s 2 k 2 s> sinh kt k s 2

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