# HP F2226A - 48GII Graphic Calculator User Manual Page 491

Graphing calculator.

Example 1 – The velocity of a moving particle v(t) is defined as v(t) = dr/dt,
where r = r(t) is the position of the particle. Let r
the transform of the velocity can be written as V(s) = L{v(t)}=L{dr/dt}= s⋅R(s)-r
Differentiation theorem for the second derivative. Let f
(df/dt)
= df/dt|
, then L{d
o
t=0
Example 2 – As a follow up to Example 1, the acceleration a(t) is defined as
2
2
a(t) = d
r/dt
. If the initial velocity is v
transform of the acceleration can be written as:
A(s) = L{a(t)} = L{d
Differentiation theorem for the n-th derivative.
(k)
k
k
Let f
= d
f/dx
|
o
t = 0
n
L{d
f/dt
Linearity theorem. L{af(t)+bg(t)} = a⋅L{f(t)} + b⋅L{g(t)}.
Differentiation theorem for the image function. Let F(s) = L{f(t)}, then
n
n
n
⋅f(t)}.
d
F/ds
= L{(-t)
–at
Example 3 – Let f(t) = e
get '1/(X+a)', or F(s) = 1/(s+a). The third derivative of this expression can
be calculated by using:
'X' ` ‚¿ 'X' `‚¿ 'X' ` ‚¿ µ
The result is
'-6/(X^4+4*a*X^3+6*a^2*X^2+4*a^3*X+a^4)', or
3
d
F/ds
L{df/dt} = s⋅F(s) - f
2
2
2
⋅F(s) - s⋅f
f/dt
} = s
= v(0) = dr/dt|
o
2
2
2
⋅R(s) - s⋅r
r/dt
}= s
, and f
= f(0), then
o
n
n
n-1
⋅F(s) – s
⋅f
−...– s⋅f
} = s
o
, using the calculator with 'EXP(-a*X)' ` LAP, you
3
4
3
2
⋅s
= -6/(s
+4⋅a⋅s
+6⋅a
.
o
= r(0), and R(s) =L{r(t)}, then,
o
= f(0), and
o
– (df/dt)
.
o
o
, then the Laplace
t=0
– v
.
o
o
(n-2)
(n-1)
– f
.
o
o
2
3
⋅s+a
4
+4⋅a
).
Page 16-13
.
o