# HP 49g+ User Manual Page 490

Graphing calculator.

An interpretation for the integral above, paraphrased from Friedman (1990),
is that the δ-function "picks out" the value of the function f(x) at x = x
delta function is typically represented by an upward arrow at the point x = x0,
indicating that the function has a non-zero value only at that particular value
of x
.
0
Heaviside's step function, H(x), is defined as
Also, for a continuous function f(x),
(
)
f
x
Dirac's delta function and Heaviside's step function are related by dH/dx =
δ(x). The two functions are illustrated in the figure below.
You can prove that
from which it follows that
where U
is a constant. Also, L
o
and
Also, using the shift theorem for a shift to the right, L{f(t-a)}=e
–as
⋅F(s), we can write L{H(t-k)}=e
e
, 1
x
H
(
x
)
, 0
x
(
)
=
(
H
x
x
dx
f
x
0
x
0
L{H(t)} = 1/s,
⋅H(t)} = U
L{U
/s,
o
o
-1
{1/s}=H(t),
-1
⋅H(t).
L
{ U
/s}= U
o
o
–ks
⋅L{H(t)} = e
–ks
. Dirac's
0
0
0
)
.
dx
–as
⋅L{f(t)} =
⋅(1/s) = (1/s)⋅e
–ks
.
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