Propiedades: Sea F (s) = L[f (t)](s) y G(s) = L[g(t)](s). 1. L[eat ] = 1 . s−a a . s2 + a2 s 3. L[cos(at)] = 2 . s + a2 2. L[sen(at)] = 4. L[tk ] = k! sk+1 , k ∈ Z. 5. L[eat f (t)] = F (s − a). 6. L[Ha (t)] = 1 −as e . s 7. L[Ha (t)f (t − a)] = e−as F (s). � �t 1 1 a 8. L[ a f (u)du] = F (s) − f (u)du. s s 0 9. L[tn f (t)] = (−1)n � dn F (s). dsn � �∞ f (t) 10. L = s F (u)du. t 11. L[f ∗ g] = F (s)G(s). 12. L[f (n) (t)](s) = sn F (s) − �n−1 j=0 sj f (n−j−1) (0+ ). 13. Si f (t) = a1 sen(at) − t cos(at), entonces L(f (t))(s) = (s2 2a2 , a �= 0. + a2 ) 2