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Elementary Laplace Transforms
f(t) = L-1(F(s)) <-> F(s) = l(f(t))
19
Mathematics
Undergraduate 2
03/26/2011
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Term
1
 Definition
1/s
Term
e^at
 Definition
1/(s-a)
Term
t^n (n = +integer)
 Definition
n!/(s^(n+1))
Term
t^p (p > -1)
 Definition
r(p+1)/(s^(p+1))
(r = gamma)
Term
sin(at)
 Definition
a/(s^2+a^2)
Term
cos(at)
 Definition
s/(s^2+a^2)
Term
sinh(at)
 Definition
a/(s^2-a^2)
Term
cosh(at)
 Definition
s/(s^2-a^2)
Term
(e^at)sin(bt)
 Definition
b/(s-a)^2+b^2
Term
(e^at)cos(bt)
 Definition
(s-a)/(s-a)^2+b^2
Term
(t^n)(e^(at)) (n = positive integer)
 Definition
n!/(s-a)^(n+1)
Term
uc(t)
 Definition
e^(-cs)/s
Term
uc(t) * f(t-c)
 Definition
e^(-cs)*F(s)
Term
e(ct)*f(t)
 Definition
F(s-c)
Term
f(ct)
 Definition
1/c * F(s/c)
Term
integral from 0 -> t
f(t-r)*g(r)dr
(r = tau)
 Definition
F(s)G(s)
Term
8(t-c)
(8 = delta)
 Definition
e^(-sc)
Term
f^(n)(t)
 Definition
s^n*F(s) - s^(n-1)f(0)-....-f(n-1)(0)
Term
(-t)^n * f(t)
 Definition
F^(n)(s)
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