Formula sheet
1
• L{1} = , s > 0.
s
n!
• L{tn } = n+1 , s > 0, n = positive integer.
s
1
, s > a.
• L{eat } =
s−a
k
• L{sin kt} = 2
, s > 0.
s + k2
s
• L{cos kt} = 2
, s > 0.
s + k2
k
• L{sinh kt} = 2
, s >| k |.
s − k2
s
• L{cosh kt} = 2
, s >| k |.
s − k2
e−cs
• L{uc (t)} =
, s > 0.
s
n
o
• L uc (t)f (t − c) = e−cs F (s).
• L{ect f (t)} = F (s − c), s > a + c.
• L{tn f (t)} = (−1)n F (n) (s), s > a.
• L{y (n) (t)} = sn Y (s) − sn−1 y(0) − sn−2 y ′ (0) − · · · − y (n−1) (0).
Z t
• f ⋆g =
f (t − τ )g(τ )dτ .
0
n
o
• L f ⋆ g = F (s) G(s).
Z T
1
• F (s) =
f (t)e−st dt, s > 0 where f (t) is a periodic function with period
1 − e−sT 0
T.
1