# HP F2226A - 48GII Graphic Calculator User Manual Page 495

Graphing calculator.

Another important result, known as the second shift theorem for a shift to the
-1
–as
⋅F(s)}=f(t-a)⋅H(t-a), with F(s) = L{f(t)}.
right, is that L
{e
In the calculator the Heaviside step function H(t) is simply referred to as '1'.
To check the transform in the calculator use: 1 ` LAP. The result is '1/X',
Similarly, 'U0' ` LAP , produces the result 'U0/X', i.e.,
i.e., L{1} = 1/s.
L{U
} = U
/s.
0
0
You can obtain Dirac's delta function in the calculator by using: 1` ILAP
The result is
This result is simply symbolic, i.e., you cannot find a numerical value for, say
'
'.
Delta(5)
This result can be defined the Laplace transform for Dirac's delta function,
-1
{1.0}= δ(t), it follows that L{δ(t)} = 1.0
because from L
Also, using the shift theorem for a shift to the right, L{f(t-a)}=e
–as
⋅F(s), we can write L{δ(t-k)}=e
e
Applications of Laplace transform in the solution of linear ODEs
At the beginning of the section on Laplace transforms we indicated that you
could use these transforms to convert a linear ODE in the time domain into an
algebraic equation in the image domain.
solved for a function F(s) through algebraic methods, and the solution to the
ODE is found by using the inverse Laplace transform on F(s).
The theorems on derivatives of a function, i.e.,
L{d
and, in general,
n
L{d
f/dt
are particularly useful in transforming an ODE into an algebraic equation.
'Delta(X)'.
–ks
⋅L{δ(t)} = e
–ks
⋅1.0 = e
The resulting equation is then
L{df/dt} = s⋅F(s) - f
o
2
2
2
⋅F(s) - s⋅f
f/dt
} = s
– (df/dt)
o
n
n
⋅F(s) – s
n-1
⋅f
−...– s⋅f
} = s
o
–as
⋅L{f(t)} =
–ks
.
,
,
o
(n-2)
(n-1)
– f
,
o
o
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