Tabela Transformada de Laplace, EDO

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UNIVERSIDADE FEDERAL DE SERGIPE
DEPARTAMENTO DE MATEMA´TICA
Disciplina: Equac¸o˜es Diferenciais Ordina´rias Turma: T01
Prof.: Adriano Veiga de Oliveira Data: 20/02/19
Tabela de Transformadas de Laplace
f(t) L {f(t)} = F (s)
1
1
s
(1)
tn (n = 0, 1, 2, . . . )
n!
sn+1
(2)
tneat (n = 0, 1, 2, . . . )
n!
(s− a)n+1 (3)
tα (α ∈ R) Γ(α+ 1)
sα+1
(4)
sin kt
k
s2 + k2
(5)
cos kt
s
s2 + k2
(6)
eat sin kt
k
(s− a)2 + k2 (7)
eat cos kt
s− a
(s− a)2 + k2 (8)
eat
1
s− a (9)
eatf(t) F (s− a) (10)
U(t− a) e
−as
s
(11)
f(t− a)U(t− a) e−asF (s) (12)
g(t)U(t− a) e−asL{g(t+ a)} (13)
tnf(t) (−1)n d
nF (s)
dsn
(14)
f ′(t) sF (s)− f(0) (15)
f ′′(t) s2F (s)− sf(0)− f ′(0) (16)
f ′′′(t) s3F (s)− s2f(0)− sf ′(0)− f ′′(0) (17)
fn(t) snF (s)− s(n−1)f(0)− · · · − f (n−1)(0) (18)
f ∗ g =
∫ t
0
f(τ)g(t− τ)dτ F (s)G(s) (19)
∫ t
0
f(τ)dτ
F (s)
s
(20)
δ(t) 1 (21)
δ(t− a) e−as (22)