Tabla de Transformadas de Laplace
L{f(t)}=Z∞
0e−s t f(t)dt
f(t)F(s)f(t)F(s)
1. 1 1
s2. tn, n = 1,2,3, .. n!
sn+1
3. tα,−1< α Γ(α+ 1)
sα+1 4. ea t 1
s−a
5. tnea t, n = 1,2,3, .. n!
(s−a)n+1 6. sin (ω t)ω
s2+ω2
7. cos (ω t)s
s2+ω28. sinh (ω t)ω
s2−ω2
9. cosh (ω t)s
s2−ω210. ea t sin (ω t)ω
(s−a)2+ω2
11. ea t cos (ω t)s−a
(s−a)2+ω212. tsin (ω t)2ω s
(s2+ω2)2
13. tcos (ω t)s2−ω2
(s2+ω2)214. sin (ω t)−ω t cos(ω t)2ω3
(s2+ω2)2
15. sin (ω t) + ω t cos(ω t)2ω s2
(s2+ω2)216. 1
a−bea t
−eb t1
(s−a) (s−b)
17. 1
a−ba ea t
−b eb ts
(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. f0(t)s F (s)−f(0)
23. f00(t)s2F(s)−s f (0) −f0(0) 24. f(n)(t)snF(s)−sn−1f(0) − · · · − f(n−1) (0)
25. ea t f(t)F(s−a) 26. tnf(t) (−1)ndn
dsnF(s)
27. Ua(t) = U(t−a)e−a s
s28. f(t−a)Ua(t)e−a s F(s)
29. f∗g=Zt
0
f(t−σ)g(σ)dσ F(s)G(s) 30. δ(t−c)e−cs
31. f(t+T) = f(t)RT
0e−s t f(t)dt
1−e−s T 32. Zt
0
f(σ)dσ 1
sF(s)
33. f(t)
tZ+∞
s
F(σ)dσ 34. f(a t)1
aFs
a
lim
s→+∞s F (s) = f(0) lim
s→0+s F (s) = lim
t→+∞f(t)
(c) Departamento de Matem´aticas. ITESM, Campus Monterrey
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