HP F2226A - 48GII Graphic Calculator User Manual page 494

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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