dictionnnaire images laplace
DESCRIPTION
dictionaire mathematiqueTRANSCRIPT
dictionnaire des images A nnée 2007/2008.
Fonction : f(t) Transformée : L (f)(p) Fonction : f(t) Transformée : L (f)(p)
1 11
peat 1
p − a
2 tnn!
pn+1tα, α > −1
Γ(α + 1)
pα+1
3 ekt sin ata
(p − k)2 + a2ekt cos at
p − k
(p − k)2 + a2
4 ekt sh ata
(p − k)2− a2
ekt ch atp − k
(p − k)2− a2
5 t sin at2ap
(p2 + a2)2t cos at
p2− a2
(p2 + a2)2
6 t e−αt 1
(p + α)2tn e−αt n!
(p + α)n+1
7 Log tΓ′(1) − Log p
p
e−at− e−bt
tLog
p + b
p + a
8 tnf(t) (−1)ndn
dpn[L (f)] (p) tf ′(t) −L (f)(p) − p
d
dp[L (f)(p)]
9 f ′(t) pL (f)(p) − f(0) f ′′(t) p2L (f)(p) − pf(0) − f ′(0)
10 f(t − α); α > 0 e−αpL (f)(p) f (n)(t) pnL (f)(p) −
n−1∑
k=0
pn−1−kf (k)(0)
11 ekt f(t) L (f)(p − k)f(t)
t
∫
∞
p
L (f)(τ) dτ
12 (f ⋆ g)(t) L (f)(p)L (g)(p)
∫ t
0
f(τ) dτL (f)(p)
p
13 f(kt); k > 01
kL (f)
(p
k
)
f(t) = f(t + ω); ω > 01
1 − eωp
∫ ω
0
e−pt f(t)dt
• limp−→∞
L (f)(p) = 0 • limp−→∞
pL (f)(p) = f(0) • (f ⋆ g)(t) =
∫ t
0
f(t − x)g(x)dx
Mr Amroun 1