# LT - cosh bt-cos bt sinh bt 4 b 3 s 4 4 b 4 15 t n n = 1 2...

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A Table of Laplace Transforms f ( t ) F ( s ) = L { f } ( s ) f ( t ) F ( s ) = L { f } ( s ) ———————————————————————————————————————————— 1. f ( at ) 1 a F ( s a ) 19. 1 t π s 2. e at f ( t ) F ( s - a ) 20. t π 2 s 3 / 2 3. f ( t ) sF ( s ) - f (0) 21. t n - (1 / 2) , n = 1 , 2 , . . . 1 · 3 · 5 ···· (2 n - 1) π 2 n s n +1 / 2 4. f ( n ) ( t ) s n F ( s ) - s n - 1 f (0) - s n - 2 f (0) 22. t r , r > - 1 Γ( r +1) s r +1 - · · · - sf n - 2 (0) - f n - 1 (0) 23. sin bt b s 2 + b 2 5. t n f ( t ) ( - 1) n F ( n ) ( s ) 24. cos bt s s 2 + b 2 6. 1 t f ( t ) s F ( u ) du 25. e at sin bt b ( s - a ) 2 + b 2 7. t 0 f ( v ) dv F ( s ) s 26. e at cos bt s - a ( s - a ) 2 + b 2 8. ( f * g )( t ) F ( s ) G ( s ) 27. sinh bt b s 2 - b 2 9. f ( t + T ) = f ( t ) T 0 e - st f ( t ) dt 1 - e - sT 28. cosh bt s s 2 - b 2 10. f ( t - a ) u ( t - a ) , a 0 e - as F ( s ) 29. sin bt - bt cos bt 2 b 3 ( s 2 + b 2 ) 2 11. g ( t ) u ( t - a ) , a 0 e - as L { g ( t + a ) } ( s ) 30. t sin bt 2 bs ( s 2 + b 2 ) 2 12. u ( t - a ) , a 0 e - as s 31. sin bt + bt cos bt 2 bs 2 ( s 2 + b 2 ) 2 13. δ ( t - a ) , a 0 e - as 32. t cos bt s 2 - b
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Unformatted text preview: cosh bt-cos bt sinh bt 4 b 3 s 4 +4 b 4 15. t n , n = 1 , 2 , . . . n ! s n +1 34. sin bt sinh bt 2 b 2 s s 4 +4 b 4 16. e at t n , n = 1 , 2 , 3 , . . . n ! ( s-a ) n +1 35. sinh bt-sin bt 2 b 3 s 4-b 4 17. e at-e bt ( a-b ) ( s-a )( s-b ) 36. cosh bt-cos bt 2 b 2 s s 4-b 4 18. ae at-be bt ( a-b ) s ( s-a )( s-b ) 37. J v ( bt ) ( √ s 2 + b 2-s ) v b v √ s 2 + b 2 , v >-1...
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