Propiedades: Sea F(s) = L[f(t)](s) y G(s) = L[g(t)](s). 1. L[e - U

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