The_Cambridge_Handbook_of_Physics_Formulas

56 Mathematics
Laplace transform pairs
f(t)=⇒ F(s)=L{f(t)} =
∫ ∞
0
f(t)e −st dt (2.524)
δ(t)=⇒ 1 (2.525)
1=⇒ 1/s (s>0) (2.526)
t n =⇒ n!
s n+1 (s>0,n>−1) (2.527)
√ π
t 1/2 =⇒
4s 3 (2.528)
√ π
t −1/2 =⇒
s
(2.529)
e at =⇒ 1
s−a
(s>a) (2.530)
te at =⇒ 1
(s−a) 2 (s>a) (2.531)
(1−at)e −at =⇒
s
(s+a) 2 (2.532)
t 2 e −at =⇒ 2
(s+a) 3 (2.533)
sinat =⇒
a
s 2 +a 2 (s>0) (2.534)
cosat =⇒
s
s 2 +a 2 (s>0) (2.535)
sinhat =⇒
a
s 2 −a 2 (s>a) (2.536)
coshat =⇒
s
s 2 −a 2 (s>a) (2.537)
e −bt a
sinat =⇒
(s+b) 2 +a 2 (2.538)
e −bt cosat =⇒
s+b
(s+b) 2 +a 2 (2.539)
e −at f(t)=⇒ F(s+a) (2.540)