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 squash@ufl.edu 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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This note was uploaded on 01/26/2012 for the course MAC 3472 taught by Professor Jury during the Fall '07 term at University of Florida.

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