Derivation of (HP) Derivatives...



#8

Hello all.

I would like to know the progression of the Symbolic Integration & Derivative capabilities from each successive generation from the 28C/S to the 50G.

To clarify the context of my question:

On the 28C, only symbolic integration of polynomials was possible. Although (and correct me if I'm wrong, please), the 28C/S was able to produce symbolic derivatives for any and all functions. Later, on the 50G, the symbolic integration is capable of producing symbolic derivatives and antiderivatives/integrals of not only polynomials but any function even those including logarithmic and trigonometric functions.

So, with that said, what was this progression of symbolic manipulation from HP-28C/S to 50G?

Thanks.

Edited: 25 May 2012, 1:59 a.m.


#9

28-> 48 -> Lonely french hackers -> 49 ->50.

TW

Edited: 25 May 2012, 2:18 a.m.

#10

data point: my HP-48SX does symbolic derivation/integration of expressions containing trig and logarithmic functions.

#11

Two side comments:

Quote:
On the 28C, only symbolic integration of polynomials was possible.

Yes, but it also had a Taylor Series Expansion capability which, coupled with the symbolic polynomial integration, did allow you to obtain an approximation to the corresponding TSE of the integral of an arbitrary function (as long as it admitted a TSE, of course) to any given degree of accuracy (subject to available memory and time, of course). In practice it was of little use.

Quote:
Although (and correct me if I'm wrong, please), the 28C/S was able to produce symbolic derivatives for any and all functions.

Sure, that's actually very easy on any machine or language as long as you've got recursion, slightly more involved without.


Quote:
Later, on the 50G, the symbolic integration is capable of producing symbolic derivatives and antiderivatives/integrals of not only polynomials but any function even those including logarithmic and trigonometric functions.

No, not "any function" but just the ones that admit symbolic integration in terms of elementary functions. This includes polynomials, rational functions of polynomials, some trigonometrics and their inverses, and some exponentials and their inverses, but it won't work on functions as simple as Sin(x2), ex2, xx, or 1/Ln(x) for instance.

Have a nice weekend.
V.


#12

Quote:
In practice it was of little use.

On playing with the HP-28S and its TSE implementation, once I found this approximation to cos(x), somewhat serendipitously:

cos(x) ~ 2 + x^4/12 + x^8/20160 - cosh(x)
which I rewrote as
cos(x) ~ 2 + x^4/12(1 + x^4/12/140) - (e^x + 1/e^x)/2
for easy programming on the HP-12C.

http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv020.cgi?read=179837

The HP-28S was my second HP calculator. Back in the day I occasionally used it to find derivatives, but I don't remember having ever used its Taylor expansion capabilities for whatever purpose.

Best regards,

Gerson.

#13

Thanks for the clarification in light of my overt accolade in the 48/50 integration capabilities.

And yes, thanks--I plan to have a great weekend. You do the same.


Edited: 25 May 2012, 2:19 p.m.

#14

Quote:


No, not "any function" but just the ones that admit symbolic integration in terms of elementary functions. This includes polynomials, rational functions of polynomials, some trigonometrics and their inverses, and some exponentials and their inverses, but it won't work on functions as simple as Sin(x2), ex2, xx, or 1/Ln(x) for instance.

Have a nice weekend.
V.


Well, in those cases, Int(f(x),x) is itself an exact symbolic integral.

This might sound like a cheat, but you can still manipulate them. Example, if you had Int(Sin(t^2),t) from 0 to x, and took the derivative with respect to x, you'd get Sin(x^2)


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