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Table of Laplace Transformsf (t ) = L-1 {F (s)} F (s) = L{ f (t )} f (t ) = L-1 {F (s)} F (s) = L{ f (t )}1. 11s2. eat1s - a3. tn , n =1,2,3,K 1!nns + 4. t p , p > -1( )11pps +G +5. t 322sp6. 1

2, 1, 2,3, tn n - = K( )121 35 2 12 n nnsp+ L -7. sin (at ) 2 2a

s + a8. cos (at ) 2 2ss + a9. t sin (at ) ( )2 2 22ass + a10. t cos (at ) ( )2 22 2 2s as a-

+11. sin (at ) - at cos (at ) ( )32 2 22as + a12. sin (at ) + at cos (at ) ( )22 2 22as

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s + a13. cos (at ) - at sin (at )( )( )2 22 2 2s s as a-+14. cos (at ) + at sin (at )( )( )2 22 2 2s s 3as a++15. sin (at + b) ( ) ( )2 2s sin b a cos bs a+

+16. cos (at + b) ( ) ( )2 2s cos b asin bs a-+17. sinh (at ) 2 2as - a18. cosh (at ) 2 2ss - a

19. eat sin (bt ) ( )2 2bs - a + b20. eat cos (bt ) ( )2 2s as a b-- +21. eat sinh (bt ) ( )2 2bs - a - b22. eat cosh (bt ) ( )2 2s a

s a b-- -23. tneat , n =1, 2,3,K ( ) 1!nns a + -24. f (ct ) 1 F sc c

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25. ( ) ( ) c ut = u t - cHeaviside Functioncsse- 26. d (t - c)Dirac Delta Functione-cs27. ( ) ( ) cut f t c - e-csF (s) 28. ( ) ( ) c ut g t e-csL{g (t + c)}29. ect f (t ) F (s - c) 30. tn f (t ), n =1, 2,3,K ( 1) ( ) ( ) - n F n s31. ( ) 1 f tt( ) sF u du 32. ( ) 0t f v dv F (s)s33. ( ) ( ) 0t f t -t g t dt F (s)G(s) 34. f (t +T ) = f (t ) ( ) 01T stsT- f t dt

- - ee35. f (t ) sF (s) - f (0) 36. f (t ) s2F (s) - sf (0) - f (0)37. f (n) (t ) snF (s) sn 1 f (0) sn 2 f (0) sf (n 2) (0) f (n 1) (0) - - - - L-- - -