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lapxform.table

# lapxform.table - Table of Laplace transforms Jonathan L.F...

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Unformatted text preview: Table of Laplace transforms Jonathan L.F. King University of Florida, Gainesville FL 32611-2082, USA [email protected] Webpage http://www.math.ufl.edu/ ∼ squash/ 9 November, 2011 (at 23:49 ) ( These notes are “In Progress”. ) General Lap xforms. With R an arbitrary real and f,g ∈ Ord( R ), ♥ 1 each formula in the table be- low holds for all s > R , unless a trailing note says otherwise. R,Q,F general reals. 7 , 9 general positive reals. N,j,k general natnums. h or h ( t ) b h or b h ( s ) C : f ~ g b f · b g Mul : f (9 t ) 1 9 · b f ( s 9 ) 1 : f s · b f ( s )- f (0) 1 N : f ( N ) s N b f ( s )- X j + k = N- 1 s j · f ( k ) (0) 1 Ply : q ( D ) ( f ) q · b f 1 1 : Z t f ( x )d x b f ( s ) /s 2 : f ( t ) · t- [ b f ] 2 N : f ( t ) · t N [ 1] N b f ( N ) 2 1 : f ( t ) /t Z ∞ s b f ( u )d u 3 : f ( t ) · e Qt b f ( s- Q ) 4 : f ( t- 7) · h ( t- 7) e- 7 s · b f ( s ) f ( t ) · h ( t- 7) e- 7 s · \ f ( t +7)( s ) 5 : f has period 7 L 7 ( f ) ( s ) [1- e- 7 s ] The “ D ” in formula (1...
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