Test1_formula_sheet

Test1_formula_sheet - Table of Laplace Transforms F (s) =...

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Table of Laplace Transforms F ( s )= L{ f ( t ) } = 8 0 f ( t ) e st dt, s > 0 L{ t p } = Γ ( p +1) s p +1 ,p> 1 , and L{ t n } = n ! s n +1 if n 0isaninteger L{ sin( at ) } = a s 2 + a 2 L{ cos( at ) } = s s 2 + a 2 L{ e at f ( t ) } = F ( s a ) ,s>a L{ u ( t a ) f ( t a ) } = e as F ( s ) ,s>a 0 L{ f ( n ) ( t ) } = s n L{ f ( t ) } s n 1 f (0) s n 2 f I (0) ··· sf ( n 2) (0) f ( n 1) (0) ,n 0 L{ t n f ( t ) } =( 1) n F ( n ) ( s ) ( 1) n d n ds n F ( s ) ,n 0 L F f ( t ) t k = 8 s F ( x ) dx L F8 t 0 f ( x ) dx k = 1 s F ( s ) L{ f ( t ) g ( t ) } L F8 t 0 f ( t x ) g ( x ) dx k = F ( s ) G ( s ) , where
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This note was uploaded on 07/16/2009 for the course MATH 3705 taught by Professor Jaberabdualrahman during the Winter '08 term at Carleton CA.

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