Tabla De Transformadas De Laplace.pdf

f (t) f (t) + g(t) cf (t) f (at) eat f (t) f 0 (t) f 00 (t) f (n) tn f (t) f (t) t

f (t − a)u(t − a) f (t)u(t − a) u(t − a) Rt f ∗ g = 0 f (τ )g(t − τ )dτ Rt f (τ )dτ 0 δ(t − t0 ) 1 t tn t−1/2 t1/2 tα sen kt cos kt sen2 kt cos2 kt eat senh kt cosh kt senh2 kt cosh2 kt teat tn eat eat sen kt eat cos kt eat senh kt eat cosh kt t sen kt t cos kt sen kt + kt cos kt sen kt − kt cos kt t senh kt t cosh kt

L{f (t)} = F (s) F (s) + G(s) cF (s) ¡s¢ 1 F a a F (s − a) sF (s) − f (0) 2 s F (s) − sf (0) − f 0 (0) sn F (s) − sn−1 f (0) − sn−2 f 0 (0) − . . . − f (n−1) (0) dn (−1)n ds F (s) R∞ n F (u)du s e−as F (s) e−as L{f (t + a)} e−as s

F (s)G(s) F (s) s −st0

e

1 s 1 s2 n!

sn+1 p π √s π 2s3/2 Γ(α+1) sα+1 , α > k s2 +k2 s s2 +k2 2k2 s(s2 +4k2 ) s2 +2k2 s(s2 +4k2 ) 1 s−a k s2 −k2 s s2 −k2 2k2 s(s2 −4k2 ) s2 −2k2 s(s2 −4k2 ) 1 (s−a)2 n! (s−a)n+1 k (s−a)2 +k2 s−a (s−a)2 +k2 k (s−a)2 −k2 s−a (s−a)2 −k2 2ks (s2 +k2 )2 s2 −k2 (s2 +k2 )2 2ks2 (s2 +k2 )2 2k3 2 (s +k2 )2 2ks (s2 −k2 )2 s2 +k2 (s2 −k2 )2

−1