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Tabla de Transformadas de Laplace L {f (t)} = ∫ ∞0 e−s t f (t) dt f(t) F (s) f(t) F (s) 1. 1 1 s 2. tn, n = 1, 2, 3, .. n! sn+1 3. tα, −1 < α Γ(α+ 1) sα+1 4. ea t 1 s− a 5. tn ea t, n = 1, 2, 3, .. n! (s− a)n+1 6. sin (ω t) ω s2 + ω2 7. cos (ω t) s s2 + ω2 8. sinh (ω t) ω s2 − ω2 9. cosh (ω t) s s2 − ω2 10. e a t sin (ω t) ω (s− a)2 + ω2 11. ea t cos (ω t) s− a (s− a)2 + ω2 12. t sin (ω t) 2ω s (s2 + ω2)2 13. t cos (ω t) s2 − ω2 (s2 + ω2)2 14. sin (ω t)− ω t cos (ω t) 2ω 3 (s2 + ω2)2 15. sin (ω t) + ω t cos (ω t) 2ω s2 (s2 + ω2)2 16. 1 a− b ( ea t − eb t ) 1 (s− a) (s− b) 17. 1 a− b ( a ea t − b eb t ) s (s− a) (s− b) 18. 1 a2 (1− cos (a t)) 1 s (s2 + a2) 19. 1 a3 (a t− sin (a t)) 1 s2 (s2 + a2) 20. f(t) + g(t) F (s) +G(s) 21. c f(t) c F (s) 22. f ′(t) s F (s)− f(0) 23. f ′′(t) s2 F (s)− s f(0)− f ′(0) 24. f (n)(t) sn F (s)− sn−1 f(0)− · · · − f (n−1)(0) 25. ea t f(t) F (s− a) 26. tn f(t) (−1)n d n dsn F (s) 27. Ua(t) = U(t− a) e −a s s 28. f(t− a)Ua(t) e−a s F (s) 29. f ∗ g = ∫ t 0 f(t− σ)g(σ)dσ F (s)G(s) 30. δ(t− c) e−c s 31. f(t+ T ) = f(t) ∫ T 0 e−s t f(t) dt 1− e−s T 32. ∫ t 0 f(σ) dσ 1 s F (s) 33. f(t) t ∫ +∞ s F (σ) dσ 34. f(a t) 1 a F ( s a ) lim s→+∞ s F (s) = f(0) lims→0+ s F (s) = lim t→+∞ f(t) (c) Departamento de Matema´ticas. ITESM, Campus Monterrey 1
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