Definite Double integral on HP50G, what am I doing wrong? I know, but really, I'm not a student. ;-)
aplnub
http://www.installuniversity.com/images/hp48/double-inner.jpg , and I
can't for the life of me to get this to work on my 50G Revision 2.08.
I have Radians and Rectangular set, with Approximate and Numeric both
checked. Anything else you need to know let me know.
My calculator just chokes on this. Minutes later, it returns no answer
but what appears to be variables replaced by the CAS system into the
equation.
I know this can be done on a 48GX because my Calculus teacher from 16
years ago, kills me to think it has been that long, did it and
correctly I might add.
This should solve to a single number. Anyone lend me a hand here?
Also, I am about to do a triple integral, any hope on the 50G?
Thanks!
aplnub
number this time. I am not sure if I corrected a flag the first time
through or not. The answer is 117.014 if anyone is interested in
solving this for fun.
Now, how do you perform this on a 48GX? I am going to pull mine out
and see which is faster. I don't think I can just place the expression
on the stack and hit EVAL for this to work like on the 50G.
John H Meyers
> http://www.installuniversity.com/images/hp48/double-inner.jpg
CASCFG 3 FIX
'\.S(0,12,\.S(0,\v/(144-SQ(Y)),\v/(1+SQ(X)/(576-SQ(X))),X),Y)'
\->NUM @ 117.014
In 15 seconds on emulated "real speed" 49G
(must be considerably faster on real 49G+/50G)
In 12 seconds on emulated "real speed" HP48GX
You might have neglected to tell the calculator
the desired precision, using FIX, SCI, or ENG
[r->] [OFF]
aplnub
decimals. 9.5 seconds on the 50G, 19 seconds on my 48GX, and less than
one second on my iPad HP48 emulator "m48." Yeah, that is what I said.
It was near instant. Crazy fast.
Thanks everyone!
On Sep 13, 7:58 pm, aplnub <apl...@gmail.com> wrote:
> I have a double integral, you can see it at this link herehttp://www.installuniversity.com/images/hp48/double-inner.jpg, and I
Tom Lake
"aplnub" <apl...@gmail.com> wrote in message
news:c8c9b0d0-35f5-47d4...@k11g2000vbf.googlegroups.com...
> Thanks to John, I got this working faster. I Fixed my output to 3
> decimals. 9.5 seconds on the 50G, 19 seconds on my 48GX, and less than
> one second on my iPad HP48 emulator "m48." Yeah, that is what I said.
> It was near instant. Crazy fast.
26 sec. to get 117.0140793 on a TI-89 Titanium HW version 3 whether in
fixed decimal mode or floating.
Tom L
Virgil
"Tom Lake" <tl...@twcny.rr.com> wrote:
On the HP series in fixed decimal mode, the fewer the digits displayed,,
the faster the calculation, and larger the potential error.
John H Meyers
> On the HP series in fixed decimal mode,
> the fewer the digits displayed,
> the faster the calculation,
> and larger the potential error.
I am designing a new calculator,
in which the number of digits per value
may be reduced to as low as zero
(twice as many, of course, per complex-valued result).
While thus giving only rough approximations
to theoretically perfect results
(which don't exist anyway, due to Quantum theory),
this does greatly speed up the computation,
as well as permitting the storage
of an infinitely large number of results :)
[r->] [OFF]
Scott Hemphill
> I have a double integral, you can see it at this link here
> http://www.installuniversity.com/images/hp48/double-inner.jpg , and I
> can't for the life of me to get this to work on my 50G Revision 2.08.
Although there may not be an exact answer in closed form in elementary
functions, there is an exact answer expressed in elliptic integrals.
Let K be the elliptic integral of the first kind, and E be the elliptic
integral of the second kind, then your double integral evaluates to:
288*sqrt(3)*(E(-1/3) - K(-1/3))
The precise value to 12 significant figures is 117.014079300.
Scott
--
Scott Hemphill hemp...@alumni.caltech.edu
"This isn't flying. This is falling, with style." -- Buzz Lightyear
m II
But only half of infinitely large when in complex-valued mode, right?
mike
eric
> aplnub <apl...@gmail.com> writes:
>
>> I have a double integral, you can see it at this link here
>> http://www.installuniversity.com/images/hp48/double-inner.jpg , and I
>> can't for the life of me to get this to work on my 50G Revision 2.08.
>
> Although there may not be an exact answer in closed form in elementary
> functions, there is an exact answer expressed in elliptic integrals.
> Let K be the elliptic integral of the first kind, and E be the elliptic
> integral of the second kind, then your double integral evaluates to:
>
> 288*sqrt(3)*(E(-1/3) - K(-1/3))
>
> The precise value to 12 significant figures is 117.014079300.
>
> Scott
My 48 returns this number in Standard: 117.014079301 Close.
eric
> aplnub <apl...@gmail.com> writes:
>
>> I have a double integral, you can see it at this link here
>> http://www.installuniversity.com/images/hp48/double-inner.jpg , and I
>> can't for the life of me to get this to work on my 50G Revision 2.08.
>
> Although there may not be an exact answer in closed form in elementary
> functions, there is an exact answer expressed in elliptic integrals.
> Let K be the elliptic integral of the first kind, and E be the elliptic
> integral of the second kind, then your double integral evaluates to:
>
> 288*sqrt(3)*(E(-1/3) - K(-1/3))
>
> The precise value to 12 significant figures is 117.014079300.
>
> Scott
My 48 returns this number in Standard: 117.014079301 Close.
Han
> Although there may not be an exact answer in closed form in elementary
> functions, there is an exact answer expressed in elliptic integrals.
The inner integral does have a closed form. (1 + x^2/(576-x^2) )
simplifies to 24^2 / (24^2 - x^2). Take the square root to get 24/
sqrt(24^2-x^2).
Use trig substitution for the inner integral (let x=24*sin(theta) ) to
get 24 * arctan( x / sqrt(24^2 - x^2) ) as an antiderivative for the
inner integral.
The result has a closed antiderivative. Apply integration by parts
from here (for the outer integral). Let u = 24 * arctan(...) and let
v' = dx. Unfortunately, the upper limit of integration sqrt(144-y^2)
from the inner integral throws a huge monkey wrench into the works,
thereby creating a much more difficult outer integral.
Han
Virgil
Scott Hemphill <hemp...@hemphills.net> wrote:
> aplnub <apl...@gmail.com> writes:
>
> > I have a double integral, you can see it at this link here
> > http://www.installuniversity.com/images/hp48/double-inner.jpg , and I
> > can't for the life of me to get this to work on my 50G Revision 2.08.
>
> Although there may not be an exact answer in closed form in elementary
> functions, there is an exact answer expressed in elliptic integrals.
> Let K be the elliptic integral of the first kind, and E be the elliptic
> integral of the second kind, then your double integral evaluates to:
>
> 288*sqrt(3)*(E(-1/3) - K(-1/3))
>
> The precise value to 12 significant figures is 117.014079300.
>
> Scott
And you did this on your HP50?
eric
group for the hp48? I have some extensive work coming up where I am
gong to need some advising through the process and would love to
through some stuff out there for help.
Although, after reading this thread, it seems that some in this thread
could handle it no problem.
Scott Hemphill
No. :-) I did it in Mathematica.
Han
> Does anyone know of a really good usenet group for calculus like this
> group for the hp48? I have some extensive work coming up where I am
> gong to need some advising through the process and would love to
> through some stuff out there for help.
>
> Although, after reading this thread, it seems that some in this thread
> could handle it no problem.
>
> On 2010-09-14 16:41:28 -0400, Virgil said:
>
> > Scott Hemphill <hemph...@hemphills.net> wrote:
>
> >> aplnub <apl...@gmail.com> writes:
>
> >>> I have a double integral, you can see it at this link here
> >>> can't for the life of me to get this to work on my 50G Revision 2.08.
>
> >> Although there may not be an exact answer in closed form in elementary
> >> functions, there is an exact answer expressed in elliptic integrals.
> >> Let K be the elliptic integral of the first kind, and E be the elliptic
> >> integral of the second kind, then your double integral evaluates to:
>
> >> 288*sqrt(3)*(E(-1/3) - K(-1/3))
>
> >> The precise value to 12 significant figures is 117.014079300.
>
> >> Scott
>
> > And you did this on your HP50?
>
>
I say just post here and there is bound to be someone interested. A
lot of avid HP users are also very strong in mathematics. Many of them
are probably even professors.