Transformata Laplace a  wzory
Tw. Heaviside a
f(t) F (s)
n

P (sk)
k
L-1{F (s)} = es t
Q (sk)
1
k=1
1
s
Tw. Cauchy ego o residuach
n!
tn
n
sn+1
L-1{F (s)} = ress=s [F (s)est]
k
k=1
1
eat
s - a
Obliczanie residuów:
w przypadku bieguna jednokrotnego:
a
sin(at)
s2 + a2
ress=s [F (s)est] = lim [(s - sk)F (s)est]
k
ssk
s
w przypadku bieguna n-krotnego:
cos(at)
s2 + a2
1 dn-1
ress=s [F (s)est] = lim [(s - sk)nF (s)est]
k
a
ssk
(n - 1)! dsn-1
sinh(at)
s2 - a2
s
cosh(at)
s2 - a2
n!
eattn
(s - a)n+1
b
eat sin(bt)
(s - a)2 + b2
s - a
eat cos(bt)
(s - a)2 + b2
eatg(t) G(s - a)
´(t) 1
´(t - a) e-as
g(t - a)1 - a) e-asG(s)
I(t
g sG(s) - g(0+)
g s2G(s) - sg(0+) - g (0+)
g " h G(s)H(s)