44
A
A
P
P
P
P
E
E
N
N
D
D
I
I
X
X
C
C
:
:
T
T
H
H
E
E
C
C
A
A
S
S
O
O
N
N
T
T
H
H
E
E
H
H
P
P
4
4
0
0
G
G
S
S
I
I
n
n
t
t
r
r
o
o
d
d
u
u
c
c
t
t
i
i
o
o
n
n
This appendix is intended to give a useful introduction and over view to the user who is new to an hp 40gs. It
is not intended to fully cover the topic, nor is it intended to serve as a reference text for the advanced user.
For those needing a far more extensive coverage than is available here, I can highly recommend the
incredibly detailed text “Computer Algebra and Mathematics with the hp 40g, Version 1.0” by Renée de
Graeve, Lecturer at the University of Grenoble and founder of the Grenoble IREM. The hp 40g was the
immediate predecessor to the hp 40gs and the CAS functions are almost identical. The only significant
difference is that on the hp 40gs you exit the CAS by pressing
HOME rather than using ON on the 40g.
Additionally, you access the CAS History using the
SYMB key on the hp 40gs rather than HOME on the 40g.
This excellent text contains a complete reference of the functions for symbolic calculation, and also
demonstrates, using many examples, how to take smart advantage of the calculating power of the hp 40g (or
hp 40gs). It can be found at Hewlett Pack
ard’s web site (http://www.hp.com/calculators
) o
r on the Help
page of The HP HOME view
(http://www.hphomeview.com
).
What is a CAS?
Although you may not have thought about it consciously, you are probably aware that most calculators do not
operate with algebra in the same way that a human does. Generally speaking solutions on computers and
calculators are found using numeric means. This is often done by using successive approximations, each one
coming closer and closer to the final answer.
You can see this process at work quite easily using the Solve aplet. All you need to do is enter an equation to
solve which is complex enough to require more than a few seconds to solve. If you do this then you can watch
the calculator work.
In the Solve aplet, enter the equation
(0, A, X
2
, X) = 1000 as shown right.
a
2
This is equivalent to solving for a in the equation:
xdx = 1000 .
∫
0
Change into the NUM view, and press on A. As soon as the
hour glass symbol appears, press the
button again. You may
need to press it more than once before the calculator takes notice, but
eventually you should see a view similar to the one right. The two values
at the top of the screen represent the calculator’s successive
approximations to the true solution.
324
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