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Formula sheet in define the laplace transform, first translation theorem, unit step functions and definition of convolutions.
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0
e−stf (t) dt.
This definition will not be provided during the quizzes/final exam.
s
for any constant C
n! sn+^
for n = 1, 2 , 3 · · ·
eat
s − a
for any constant a
k s^2 + k^2
for any constant k
s
s^2 + k^2
for any constant k
k s^2 − k^2
for any constant k
s
s^2 − k^2
for any constant k
f (n)(t)
= snF (s) − sn−^1 f (0) − sn−^2 f ′(0) − · · · − f (n−1)(0)
eatf (t)
= F (s)|s→s−a where F (s) = (^) L {f (t)}
0 if 0 ≤ t < a 1 if t ≥ a
g(t) if 0 ≤ t < a h(t) if t ≥ a
⇒ f (t) = g(t) − g(t) (^) U (t − a) + h(t) (^) U (t − a)
This formula will not be provided during quiz/examination.
g(t) if 0 ≤ t < a h(t) if a ≤ t < b j(t) if t ≥ b
⇒ f (t) = g(t) − g(t) (^) U (t − a) + h(t) (^) U (t − a) − h(t) (^) U (t − b) + j(t) (^) U (t − b)
This formula will not be provided during quiz/examination.
This formula is easier to apply for finding inverse-Laplace transform.
This formula is easier to apply for finding Laplace transform.
e−as s
dn dsn^
F (s) where F (s) = (^) L {f (t)}
∫^ t
0
f (τ )g(t − τ ) dτ
∫^ t
0
f (τ ) dτ
F (s)
s
L {f^ (t)}^ =^
1 − e−sT
0
e−stf (t) dt