HP-48GX symbolic integral?
Indifference
you take a symbolic integral without specifying any bounds, you know, like
the TI-89. If it can, I might go for a 48G+ rather than a TI-89. I've heard
that the HP is better in all respects except this.
--
Indifference
ind...@usa.net
Jemfinch02
>you take a symbolic integral without specifying any bounds, you know, like
>the TI-89.
On a stock HP, you would have to set the limits of your integral from 0 to X,
and integrate. Unfortunately, the HPs intrinsic symnbolic integration engine
is based on technology from 13 years ago and is therefore very primitive
(french speakers will have to pardon the pun)
Actually,though, you wouldn't have to write a program because the algebra
libraries already exist. Erable (the best CAS for the HP, and it's free) has
an indefinite integration program that is partially based on the Risch
algorithm. What this means is that some integrals can be solved by Erable that
are not solved by the TI-89/92. I have experienced some problems integrating
trigonometric functions in that the answer I received often is not in the form
I would like to see it in. There are programs in Erable that will change forms
and such, but I am still trying to learn them.
> I've heard
>that the HP is better in all respects except this.
If you want the full breakdown of what I have noticed in comparing the HP48
with its programs to the TI-89 as it comes from the factory, here you go:
The HP48 does unlimited precision arithmetic. What this means is that if I
want to know what 350! is, I can know it. Every digit of it. I haven't seen
the TI-89 do that.
The HP48 handles imaginary numbers better. Just today, I tried to raise i to
the i power on a TI-89 and got a domain error. On the HP, it returns the true
value: i^i = e^(-pi/2)
The TI-89 graph is faster than the HP. I have not tried many speedy graphing
programs on the HP, though, so this may not be a real concern.
The TI-89 does symbolic integration better. Sure, the Risch algorithm will
catch some stuff that the TI-89 does not do, but these integrals are by and
large not useful to a student.
The TI-89 is faster. On my HP48G, with only 32k of ram, I could not take a
taylor polynomial past the 8th degree of e^(x^2). It would calculate for about
10 minutes on the 9th degree and then poop out with a "insufficient memory"
message. Note, however, that this is my HP48G. I have not tried this on my
GX. Also, though, the TI-89 would find 20th degreee taylor approximations in
about the time my HP48 took for a 5th degree.
There is FAR more user support for the HP48 than for any TI-calculator. If you
have a question and you post it, I guarrantee within a day or two you will have
the answer you were looking for. People will write entire programs to help you
out. The programs and libraries for the HP48 outshine anything I have ever
seen for the TI-89, also.
From what I have seen, most people using the TI-89 are students--in either
college, or even more likely, in high school. The people who use the HP48 are
the computer science gurus, the mathematics professors, the professional
researchers, and the engineers. This group of people, from what I have seen,
are more mature and definitely more helpful than the TI-89 users. They also
write FAR better programs :-)
If I find some more differences that aren't obvious from the packaging or the
informational websites, feel free to ask.
If you'd like to see the kind of support that exists for the HP48, go to
www.hpcalc.org and browse through the programs and reviews and such there. It
could take you days to go through it all, but at least you'll see the kind of
support the HP48 has. Imagine how much support the next HP should have!
Hope it helps,
Jeremy
Joseph Duncan
your upper limit to the variable you are integrateing....
but then you get to a point whare u want to do some more complex math and you
need to get erable an alg48......
out
Joseph
Indifference wrote:
> I was just wondering, is it possible to write a program for the 48 that lets
> you take a symbolic integral without specifying any bounds, you know, like
> the TI-89. If it can, I might go for a 48G+ rather than a TI-89. I've heard
> that the HP is better in all respects except this.
>
> --
> Indifference
> ind...@usa.net
sharif...@ameritech.net
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Jemfinch02
>need to get erable an alg48......
Erable will help; Alg48 does not do much for integration except add the
rational function functionality. If I understood the documentation to Alg48
correctly, it adds very little functionality to the HP48's intrinsic
integration capabilities.
Jeremy
Steen Schmidt
does symbolic integration pretty well.
Ice
Jemfinch02 skrev i meddelelsen
<19990416233939...@ng26.aol.com>...
Jemfinch02
>>rational function functionality. If I understood the documentation to
>Alg48
>>correctly, it adds very little functionality to the HP48's intrinsic
>>integration capabilities.
>Yes. But you can get the INT library if you use ALG48. It's a library that
>does symbolic integration pretty well.
Yes, I was speaking of the INT library. As I understood the documentation,
there is still very little functionality added to the calculator's own
integration capabilities.
Jeremy
Joseph Duncan
Jemfinch02 wrote:
> >but then you get to a point whare u want to do some more complex math and you
> >need to get erable an alg48......
>
> Erable will help; Alg48 does not do much for integration except add the
> rational function functionality. If I understood the documentation to Alg48
> correctly, it adds very little functionality to the HP48's intrinsic
> integration capabilities.
>
> Jeremy
ya but back in the day when i was take lower calc cources in highschool our
teachers would like to have us simplify everything...... so alg48 was very usefull
for me at least, and then when i went on to college erable became a much loved
tool and it still will be when i take mth 255 and 256...
Carlos Bazzarella
Very good comparison list. I would just like to make one comment for
the next HP calc.
> >I was just wondering, is it possible to write a program for the 48 that lets
> >you take a symbolic integral without specifying any bounds, you know, like
> >the TI-89.
>
> On a stock HP, you would have to set the limits of your integral from 0 to X,
> and integrate. Unfortunately, the HPs intrinsic symnbolic integration engine
> is based on technology from 13 years ago and is therefore very primitive
> (french speakers will have to pardon the pun)
>
> Actually,though, you wouldn't have to write a program because the algebra
> libraries already exist. Erable (the best CAS for the HP, and it's free) has
> an indefinite integration program that is partially based on the Risch
> algorithm. What this means is that some integrals can be solved by Erable that
> are not solved by the TI-89/92. I have experienced some problems integrating
> trigonometric functions in that the answer I received often is not in the form
> I would like to see it in. There are programs in Erable that will change forms
> and such, but I am still trying to learn them.
And here it is :
The integration algorithm for Trigonometric functions should return the
answer in the most expected form; the one that is usually provided in
calculus textbooks. This is necessary to validate that the student's answers
are correct as well as to minimize complicated transformation commands
that users never seem to learn and just complicate the machine's operation.
Carlos.
Jemfinch02
>> trigonometric functions in that the answer I received often is not in the
>form
>> I would like to see it in. There are programs in Erable that will change
>forms
>> and such, but I am still trying to learn them.
>The integration algorithm for Trigonometric functions should return the
>answer in the most expected form; the one that is usually provided in
>calculus textbooks. This is necessary to validate that the student's answers
>are correct as well as to minimize complicated transformation commands
>that users never seem to learn and just complicate the machine's operation.
I do completely agree. Not to reduce my thankfulness to M. Bernard in the
least, but I don't quite understand how to use the trigonometric identity
programs. If there's any way a small faq, manual, examples, etc. could be
written to supplement the documentation, I would be even more appreciative than
I am now (which is still quite a bit).
Thanks,
Jeremy
Virgil
>And here it is :
>
>The integration algorithm for Trigonometric functions should return the
>answer in the most expected form; the one that is usually provided in
>calculus textbooks. This is necessary to validate that the student's answers
>are correct as well as to minimize complicated transformation commands
>that users never seem to learn and just complicate the machine's operation.
>
>
>Carlos.
That is exactly the wrong attitude. It would be better if calculators
never gave exactly the same form of answer as textbooks, but required a
little metal activity from the student, as well as the exercise of his/her
fingers.
--
Virgil
vm...@frii.com
Jemfinch02
I respectfully disagree. Complicated and arcane procedures do not constitute
mental activity. I use my calculator on homework as previously mentioned to
validate answers. I have my calculator on tests as a backup in case for some
reason my mind isn't working correctly, or if I get stumped. These situations
are cases in which the calculator would be more useful if it returned the form
most likely to be in a calculus book or test.
Imagine if all technology was arbitrarily limited in it's capabilities because
the advance of technology reduces the amount of work necessary by the human.
Progress would halt. Anytime technology comes up with some way of decreasing
the amount of work involved in some action, it makes up for it by increasing
capabilities in other areas. To arbitrarily reduce the capabilites of a
calculator so that students will have t think is ludicrous. Increase the
capabilities; allow the students to use them; watch the students and teachers
find more work for themselves while they revel in new technology.
I hope this made sense. It's late at night. :-)
Jeremy
Bernard Parisse
for integration. For the same integral you will see different answer
depending on the author's preferred integration method. Why? Because
there is no standard change of variable for each type of integrals.
There are many, for example for trigo fractions, you can use u=exp(ix)
or u=tan(x/2) and based on parity of the integrand you can sometimes
use u=sin(x) or u=cos(x) or u=tan(x). None of them is better in all
situations, sometimes the first is better, sometimes the second one,
....
A CAS, especially Erable which is not built-in, must choose one of them
because of memory constraint. Hence you will have either to do a change
of variables by hand or know how to compare the answer given by the CAS
and the answer of your textbook.
Bernard Parisse
Carlos Bazzarella
>
> In article <371B3A...@poliplus.com>, cba...@poliplus.com wrote:
>
> >And here it is :
> >
> >The integration algorithm for Trigonometric functions should return the
> >answer in the most expected form; the one that is usually provided in
> >calculus textbooks. This is necessary to validate that the student's answers
> >are correct as well as to minimize complicated transformation commands
> >that users never seem to learn and just complicate the machine's operation.
> >
> >
> >Carlos.
>
> That is exactly the wrong attitude. It would be better if calculators
> never gave exactly the same form of answer as textbooks, but required a
> little metal activity from the student, as well as the exercise of his/her
> fingers.
This is like saying if you use your calculator to calculate (hence the name)
5 times 4 that it is the wrong attitude if you get the expected 20. I know
this is a stretch since in algebra (trig) you have different forms for the
same thing but the default answer should always be the familiar answer.
Carlos.
Carlos Bazzarella
>
> >In article <371B3A...@poliplus.com>, cba...@poliplus.com wrote:
> >
> >>And here it is :
> >>
> >>The integration algorithm for Trigonometric functions should return the
> >>answer in the most expected form; the one that is usually provided in
> >>calculus textbooks. This is necessary to validate that the student's answers
> >>are correct as well as to minimize complicated transformation commands
> >>that users never seem to learn and just complicate the machine's operation.
> >>
> >>
> >>Carlos.
> >
> >That is exactly the wrong attitude. It would be better if calculators
> >never gave exactly the same form of answer as textbooks, but required a
> >little metal activity from the student, as well as the exercise of his/her
> >fingers.
> >
> >Virgil
>
> I respectfully disagree. Complicated and arcane procedures do not constitute
> mental activity.
I couldn't have said it better myself !!!
> I use my calculator on homework as previously mentioned to
> validate answers. I have my calculator on tests as a backup in case for some
> reason my mind isn't working correctly, or if I get stumped. These situations
> are cases in which the calculator would be more useful if it returned the form
> most likely to be in a calculus book or test.
>
> Imagine if all technology was arbitrarily limited in it's capabilities because
> the advance of technology reduces the amount of work necessary by the human.
> Progress would halt. Anytime technology comes up with some way of decreasing
> the amount of work involved in some action, it makes up for it by increasing
> capabilities in other areas. To arbitrarily reduce the capabilites of a
> calculator so that students will have t think is ludicrous. Increase the
> capabilities; allow the students to use them; watch the students and teachers
> find more work for themselves while they revel in new technology.
>
> I hope this made sense. It's late at night. :-)
This makes perfect sense to me, you got some pretty good points.
Carlos.
Carlos Bazzarella
>
> I would like to emphasize that calculus book do not have a standard
> for integration. For the same integral you will see different answer
> depending on the author's preferred integration method. Why? Because
> there is no standard change of variable for each type of integrals.
> There are many, for example for trigo fractions, you can use u=exp(ix)
> or u=tan(x/2) and based on parity of the integrand you can sometimes
> use u=sin(x) or u=cos(x) or u=tan(x). None of them is better in all
> situations, sometimes the first is better, sometimes the second one,
I can only partially agree with you here. Open several textbooks and
you will find that there ARE standard subs for certain types of
integrals. Math is basically a pattern matching and processing discipline.
A student can only say she/he knows how to integrate if she/he can
look at an integral and know what type of method to apply. Some problems
typically have multiple ways of solving it but a good math student know
the easiest way to solve it. Of course I am talking about pedagogically
correct methods and not algorithmically computer based methods.
The sub you mentioned u=exp(ix), I've never seen in any textbook I've
come across. You can look at a trig fraction and easily determine
whether to use u=cos(x) or u=tan(x/2). This is Math knowledge that
must be embedded into the CAS.
> ....
> A CAS, especially Erable which is not built-in, must choose one of them
> because of memory constraint. Hence you will have either to do a change
> of variables by hand or know how to compare the answer given by the CAS
> and the answer of your textbook.
You are absolutely right here though. In small devices it is vital to
balance functionality with memory constraints.
Here is a completely unrelated question : Does anyone know if HP is
announcing anything on this week's 77th Annual NCTM (National Council
of Teachers of Mathematics) conference being held in San Francisco ?
Carlos.