Tabela 1. Lapaceova transformacija elementarnih funkcij
f(t) F(s) f(t) F(s)
1 H(t) 1
s 2 tn n!
sn+1
3 eat 1
s−a s > a 4 H(t−a) 1
se−at a >0
5 sin(at) a
s2+a2 6 cos(at) s
s2+a2
7 teat 1
(s−a)2 s > a 8 tsin(at) 2as
(s2+a2)2 9 tcos(at) s2−a2
(s2+a2)2 10 1
2(sin(at)−atcos(at)) a3 (s2+a2)2
11 δ(t) 1 12 δ(t−a) e−as a >0
Tabela 2. Lapaceova transformacija pravila
f(t) F(s)
i af(t) aF(s)
ii f(t) +g(t) F(s) +G(s)
iii f(at) 1
aF(s
a) a >0
iv H(t−a)f(t−a) e−asF(s) a >0
v eatf(t) F(s−a) s > a
vi f0(x) sF(s)−f(0)
vii f(n)(t) snF(s)−sn−1f(0)−sn−2f0(0)− · · · −fn−1(0)
viii tf(t) −F0(s)
ix tnf(t) (−1)nF(n) x
Z t
0
f(τ)dτ 1
sF(s) xi 1
tf(t)
Z ∞
s
F(σ)dσ xii
Z t
0
f(τ)g(t−τ)dτ F(s)G(s)
xiii f(0) = lim
s→∞(sF(s)) lim
t→∞f(t) = lim
s→0(sF(s))