The power of the 49g+ over the TI-89



#12

On Friday in Calculus II, we were covering integrals which are generally done by looking at tables or solved using a CAS (computer algebra systems). The other 17 people in my class (though about 4 of them use HP scientific calculators) use the TI-89 as their primary calculator. I use my 49g+. So, we were working problems as a class, and so everyone was punching them into their calculator. My teacher (who really likes the HP calculators) would get the answer from the TI-89 first, and then from my 49g+. For every single one of the integrals we did, the 89 would return an answer which was several screens long (very very very large answers). My calculator would consistently return a 1 or 2 term answer. Everyone would ask, "How does it do that?!? My answer takes the whole board (literally), and his answer is tiny."

It was really quite funny. And I didn't even bring up the trying to add 1 to 1000! (to add 1 to a large number, it takes the 89 about 30 seconds... the 49g+ does it instantly)

-Ben Salinas
12345


#13

Ben --

I'd be interested to see the difference in performance of symbolic calculus between the HP-49 and TI-89 series models. I have a 49G, but I'd doubt that the 49G+ is any different.

Can you provide several of the integral problems in question?

On the second item, (1000! + 1), I assume that "exact" mode is required; the result exceeds 10500. Please see also the "hp 49g+" thread stated by Pascal Jerney, immediately below this thread.

-- KS

Edited: 16 Oct 2004, 4:39 p.m.


#14

Sure. The examples we did were as follows:

sin^2(x)*cos^3(x)
(x^2)*SQRT(A^2+x^2)
(arccos(ax))^2

I am sure there are countless other examples that would also illustrate the point.

I believe that the 89 just uses a ported version of Derive. I guess that just goes to show you that actually writing your own software yields better results.

-Ben


#15

You are correct, the TI CAS caluclators use Derive.


Performance notes:

For TI: TI-89 Titanium using 2nd Integral command
For HP: HP-49G+ Use SYMB-CALC-INTVX command; Real Mode

1. integral((sin x)^2 * (cos x)^3) = -((sin x)^5 ÷ 5 - (sin x)^3 ÷ 3)
TI was slightly faster, but HP's answer was more simplified.

2. integral(x^2 * sqrt(x^2 + a^2))
TI returned (-a^4 * ln(sqrt(x^2+a^2)+x)÷8 + (x*(x^2+a^2)^1.5)÷4 - (a^2*x*sqrt(x^2+a^2))÷8

HP returned


Both returned the answer in the same time, with both answers several screens long.

3. integral(acos(a* x)^2)
TI returned (4*a*x*(asin(a*x))^2 + 4*(2*sqrt(1-a^2*x^2)-a*pi*x)*asin(a*x)-4*pi*sqrt(1-a^2*x^2)+a*(pi^2-8)*x)÷(4*a)

HP returned -(2*acos(x*a)÷a*sqrt(-(x^2*a^2-a))) + (acos(x*a)^2 -2)÷a *x *a

TI was slightly faster, but returned the answer in one fraction, as apposed to HP "breaking up" the fraction into a few terms. The latter I think is easier to read.

#16

Being a great fan of HP calculators I however still regard Derive as one of the better DOS programs ever written...

Best regards,
Erik Ehrling (Sweden)


#17

Actually, the TI CAS is not Derive, but a similar program written by the authors of Derive.

Similar, but not the same.

#18

IMHO, it would have been a much better exercise if the task was to solve these integrals without a calculator or a computer. The class would have learned much more.

It is not easy to understand (at least for me) what is the point in solving integrals in the classroom by typing them either into a TI89, or a HP49G+, or Derive on PC, or Mathematica, or naything else? You do not see all the necessary transformations needed to find the solution out.

Maybe, I am a bit old-fashioned...


#19

Hi Nenand. Maybe you and I belong in a different museum (one with dinosaurs) because I agree with your questioning the use of calculators for this purpose. With my 3 children I have emphasized doing math with pencil and paper and only using a calculator to check arithmetic. Thus far, this philosophy has served them well. However, the world around us is changing and who knows, in the future the student that succeeds may be the one who enters numbers or equations into a calculator or computer the quickest.

Regards,

John


#20

Hi John,

[qoute] ...in the future the student that succeeds may be the one who enters numbers or equations into a calculator or computer the quickest.

[/quote]

Well, this is true for the "Student"--but not for the person, in the "real world."

In the Real World, you have to figure it out for yourself---and if you don't understand the problem or how to construct a solution, then you are SOL.

I hope we are not dinosaurs---I would rather be an opthalmasaurus, or a pterosaur or something......

Best regards,


Bill

#21

I agree...

The focus of most of calculus I and calculus 2 thus far has been doing calculus without relying on the crutch of a calulator. This is why we have done integrals by hand for a total of about 3 months time, and solely with a calculator for 1 period.

-Ben Salinas
12345

#22

Hi Ben!

Hey, why don't you try (numerically) integrating in class with the 15C? Now THAT whould make an impression :^)

Best regards,

Bill


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