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I'm teaching 4th quarter calculus and recently began covering triple integrals. The students are able to set up the integrals just fine now; change the order of integration; calculate center of mass and moments of intertia, etc. Obviously the problems need to be "reciped" to be easily integrable by hand (I'm also having them number crunch harder ones with Mathematica). Several students want to try and have their calculators evaluate the integrals after they set them up...which brings me to the question,
It seems the TI89 can numerically calculate most of the integrals in a few seconds. BUT, the HP50's are taking several minutes, if not hours. I had one running for twoplus hours and had to abort it. I set the 50G on approximate, and set the tolerance (error) down to .001, and still nothing after an hour.
Are there other settings I'm overlooking, or is the HP50 just not up to the task of triple integrals?
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HI;
do you have any online working material that can be shared, or any specific example? This way we (any of us) could try some of them and see what happens our own. Results would be post as they come out. Do you agree with this?
Cheers.
Luiz (Brazil)
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Hi Luiz. I don't have the exact one in front of me (or my 50g either) but if I recall correctly this is the one the TI promptly calculated, and the 50g was aborted after 2 hours:
\ 2 \ 42x \ 42xy
  
   6xy dz dy dx = 64/5
  
\ 0 \ 0 \ 0
It's much easier to do by hand than to get it all typed into a calculator (or computer) and wait.
Cheers,
CHUCK
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Well, the example you gave just took 20 seconds on my old HP49G. I guess it would take much less on a HP50G.
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On the TI 89 Titanium it took me about 2 minutes to key it in, because I first had to remember the order of keying in the limits and variables. The calculation took maybe 2 seconds.
On my Casio Algebra FX 2.0 plus it's pretty much the same input syntax and response time.
On the HP 50G it was much easier to key in with the equation writer, maybe under 30 seconds. First I calculated in approximate mode and aborted it after some minutes. Then I changed to exact mode and the result came after 6 seconds.
As an aside: in the equation writer you have to key in 6X*Y, explicitly multipliying X and Y, else you would have keyed in the variable "XY".
Edited: 31 Oct 2007, 6:02 a.m.
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Quote:
Hi Luiz. I don't have the exact one in front of me (or my 50g either) but if I recall correctly this is the one the TI promptly calculated, and the 50g was aborted after 2 hours:
\ 2 \ 42x \ 42xy
  
   6xy dz dy dx = 64/5
  
\ 0 \ 0 \ 0
My 50G took about 8 seconds to evaluate the above integration to a solution of 64/5.
Although I freely admit to a very limited understanding of triple integrations...namely, how can we integrate with respect to Z when Z doesn't appear in the expression being integrated. Also, do dz dy dx correspond to the three integrals from left to right, or in an innermost/innermost, outermost/outermost relationship. Any help appreciated. Best regards, Hal
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Quote:
namely, how can we integrate with respect to Z when Z doesn't appear in the expression being integrated. Also, do dz dy dx correspond to the three integrals from left to right, or in an innermost/innermost, outermost/outermost relationship. Any help appreciated.
a) the integral of z dz would be 1/2 z^{2}. By the same rule, the integral of 1 dz would be just z.
b) the integral sign and the d are like parentheses. Inner most intergral sign corresponds to inner most d, middle integral sign corresponds to middle d and outer most integral corresponds to outer most d.
Edited: 31 Oct 2007, 5:25 a.m.
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With my 50g set to Exact mode, it processed the expression in approx 5 seconds and produced 64/5.
Then, with it set to approximate mode, Number Format FIX 1, it took about 13 seconds to produce the value 12.7.
With it set to FIX 2, it took approximately a minute to produce 12.8.
I don't understand the differences completely, but I understand that in exact mode it handles things symbolically but in approx mode it uses some kind of incremental loop to approximate the value. I think the step on the loop is determined by the resolution needed.
This is only my opinion, but I know there the folks in this forum have more insight to offer on this issue.
Very Respectfully,
David
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Hi,
Just for the record, the following HP71B code:
10 DEF FNF(X,Y,Z)=6*X*Y
20 DEF FNG(X,Y)=INTEGRAL(0,42*XY,H,FNF(X,Y,IVAR))
30 DEF FNH(X)=INTEGRAL(0,42*X,H,FNG(X,IVAR))
40 H=.01 @ DISP INTEGRAL(0,2,H,FNH(IVAR))
>RUN
12.80
produces the correct answer in FIX 2 in 0.76 seconds under Emu71 on an old laptop, or 3 minutes in a physical HP71B.
The template used is general, just replace your f(x,y,z) and limits (shown in bold) in the above code to compute any other triple integral.
Best regards from V.
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Hi Valentin,
if we decide to use PC power (EMU71), the free Eigenmath will do it with this input
defint(defint(defint(6*x*y,z,0,42*xy),y,0,42*x),x,0,2)
in about 0.00001 second. ;)
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on my 48GX it took 15 min at FIX4 to come out with 12.8000
amazing how fast these newer calcs actually are.
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Quote:
amazing how fast these newer calcs actually are.
I didn't find out how long the 50G takes in approximate mode and fix 4 because I interrupted it after 2 or 3 minutes. The 6 seconds from my post above were achieved in exact mode.
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Well, my 50g is still not integrating it. I have it set to FIX 3, approximate, tried both complex and real mode, modulo flags, etc. Still no answer after several minutes.....
[edit]
Ah Ha!!!!!! Taking it off approximate mode worked! 65/5 in 5 seconds!!!
Thanks everyone for trying this out. I find it odd that it will calculate the exact answer but not an approximate answer. Hmmm. Suppose the integrand did not have an antiderivative. Would it not be able to give a 3place approximiate value in a respectable amount of time? I find this rather limiting.
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Thanks Meenzer. The approximate mode worked! Still a little frustrating that the algorithm for approximate mode takes an eternity.
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At first, I thought that was a limitation too. But, after donig some comparisons with a TI83+, I started seeing the beauty of it. I found that the TI didn't maintain it's accuracy past 3 decimal places (for the ingetral I was attempting).
I'd much rather have slow and certain than fast and "best guess". I'll see if I can't dig up some examples to post here,
Very Respectfully,
David
