1
Q
u(t) (Heaviside function)
A
1, t>0
0, t<= 0
1
Q
delta(t) (Dirac delta function)
A
0, t != 0
inf, t =0
2
Q
L{C}
A
C/s
3
Q
L{f(t)} (F(s))
A
int [0, inf): e^(-st) * f(t) dt
4
Q
L{t}
A
1/(s^2)
5
Q
L{t^n}
A
n! / [s^(n+1)]
6
Q
L{e^(-at)}
A
1/(s+a)
7
Q
L{sin(wt)}
A
w/ [s^2 - w^2]
8
Q
L{cos(wt)}
A
s/ [s^2 - w^2]
9
Q
L{u(t-a)}
A
[e^(-as)] / s
10
Q
L{delta(t)}
A
1
11
Q
L{delta(t-a)}
A
e^(-as)
12
Q
L{erf(t/2a)}
A
1/s * e^(as)^2 * erf(as)
a >= 0
13
Q
L{f(at)}
A
1/a * F(s/a)
a > 0
14
Q
L{f(t-a) * u(t-a)}
A
e^(-as) F(s)
15
Q
L{e^(-at) * f(t)}
A
F(s + a)
16
Q
L{g^(n) of (t)}
A
s^n * G(s) - s^(n-1) g(0) - s^(n-2) g’(0) - … - g^(n-1)(0)
17
Q
L{(f*g)(t)}
A
F(s) * G(s)
18
Q
L{ t * f(t) }
A
-F’(s)
19
Q
L{ t^n * f(t) }
A
(-1)^n * (nth derivative)F(s)
20
Q
L{ int[0, x]: f(t) dt }
A
1/s * F(s)
MATH 204
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