HP 50g User Manual Page 490

Graphing calculator.

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:
Differentiation theorem for the n-th derivative.
(k)
k
Let f
= d
o
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 d
n
n
ds
= L{(-t)
f(t)}.
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
Now, use '(-X)^3*EXP(-a*X)' ` LAP μ. The result is exactly the same.
Integration theorem. Let F(s) = L{f(t)}, then
Convolution theorem. Let F(s) = L{f(t)} and G(s) = L{g(t)}, then
A(s) = L{a(t)} = L{d
k
f/dx
|
, and f
t = 0
n
n
n
L{d
f/dt
} = s
F(s) – s
–at
, using the calculator with 'EXP(-a*X)' ` LAP, you
3
3
d
F/ds
= -6/(s
t
L
f
0
= v(0) = dr/dt|
o
2
2
2
r/dt
}= s
R(s) - s r
= f(0), then
o
n-1
f
...– s f
o
4
3
2
2
+4 a s
+6 a
s
1
(
)
(
u
du
F
s
, then the Laplace
t=0
– v
.
o
o
(n-2)
(n-1)
– f
.
o
o
3
4
+4 a
s+a
).
).
s
n
F/
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