Putting Casio fx-991CW in perspective.

[Matt Agajanian]

Hi all.

Call it what you will (blunder, disappointment, several steps backward, a flop, woefully inadequate, etc). Perhaps even to put it on par with the first & second editions of the 115ES let alone the 991ES editions, the CW falls short.

Rather than use it as a paperweight, do you see the CW having any merits, applications, benefits?

[lrdheat]

I do like that it uses 22 or 23 digits internally, produces exact fractions, pi multiples or fractions more often than other machines. When integrating near a discontinuity/vertical asymptote, one can integrate using a lower or upper limit 1*10^-17 or -18 from the vertical asymptote and get a very accurate result. From a statistics point of view, retention of data when changing modes or powering off is very welcome.

[carey]

(09-20-2023 07:07 AM)Matt Agajanian Wrote:  Hi all.
...do you see the CW having any merits, applications, benefits?

Here's a novel 991CW application: manual iteration to solve a transcendental equation using the 991CW's composite functions.

The simple looking transcendental equation, e^-x = x, is unsolvable in closed form (try it!). While easy to solve using a graphical calculator by plotting both the LHS and RHS and finding their intersection, equations such as this can also be solved by iteration, e.g., selecting a value for x, calculating e^-x (which becomes the new value of x), rinse and repeat, with the values, if plotted, forming a cobweb plot.

An iterative solution can be found using a spreadsheet like Excel or Google Sheets that permits circular references by selecting the iteration option and limiting the number of iterations (to prevent infinite loops). However, I've not found a calculator spreadsheet (including the 991CW spreadsheet) that allows circular references.

On the 991CW one can use manual iteration via composite functions to work around the circular reference issue, and without a spreadsheet, as follows:

1) From Home, highlight Calculate, click EXE and click Function.
2) Highlight Define f(x), enter e^-x, and click EXE.
3) Click Function, highlight Define g(x), click EXE, click x, and click EXE.
4) Click Variable, highlight x, enter 0.5 as an initial guess, click EXE.
5) Click Home, highlight Calculate, click EXE, click Function, highlight f(x) and complete "f(" by clicking "x" and entering ")" to get "f(x)" and select EXE.

The first iterate 0.6065306597 is displayed. To manually obtain subsequent iterates, the steps are simply as follows.

6) Click Variable, highlight x, click EXE, highlight STORE, click EXE, and the first iterate becomes the new value of x.
7) Click EXE again to update the value of f(x) and obtain the 2nd iterate: 0.5452392119
8) Repeat steps 6 and 7 to obtain the remaining iterates.

The first 12 iterates (sufficient to achieve convergence to within 0.001) are as follows (if no transcription errors).

1) 0.6065306597
2) 0.5452392119
3) 0.5797030949
4) 0.5600646279
5) 0.571172149
6) 0.564862947
7) 0.5684380476
8) 0.5664094527
9) 0.5675596343
10) 0.5669072129
11) 0.567277196
12) 0.5670673519

Wolfram Alpha gives the solution as 0.567143.

[klesl]

A small modification of procedure written above
7) Click EXE again to update the value of f(x) and obtain the 2nd iterate: 0.5452392119
8) recall f() and insert ans, so you get f(ans) and press OK or EXE several times
the final result is 0,567143xxxx

[carey]

(09-23-2023 02:20 PM)klesl Wrote:  A small modification of procedure written above
7) Click EXE again to update the value of f(x) and obtain the 2nd iterate: 0.5452392119
8) recall f() and insert ans, so you get f(ans) and press OK or EXE several times
the final result is 0,567143xxxx

That's a huge improvement, requiring only repeated EXE presses to obtain the next iterate! Thank you for suggesting it!

[Csaba Tizedes]

MoHPC don't like Youtube shorts....

The link: https://www.youtube.com/shorts/1R3IMq227dM

https://www.youtube.com/shorts/1R3IMq227dM

[Csaba Tizedes]

Same, without d/dx()

https://www.youtube.com/shorts/-8pGxTXSk40

https://www.youtube.com/shorts/-8pGxTXSk40

[Eddie W. Shore]

My favorite addition is the ability to access two functions f(x) and g(x) from anywhere.

The store button/function needs to come back. And the multistate colon.

[carey]

(09-23-2023 05:19 PM)Csaba Tizedes Wrote:  MoHPC don't like Youtube shorts....

The link: https://www.youtube.com/shorts/1R3IMq227dM

https://www.youtube.com/shorts/1R3IMq227dM

(09-23-2023 05:21 PM)Csaba Tizedes Wrote:  Same, without d/dx()

https://www.youtube.com/shorts/-8pGxTXSk40

https://www.youtube.com/shorts/-8pGxTXSk40

Csaba,

These videos are great -- very nicely done! Thank you for sharing them!

A quick question about Newton's method (shown in the videos). Newton's method has stood the test of time and has sound justification in Taylor series. Of the dozens* of other root-finding methods that have been developed over the years, some general and some claiming to have advantages in special situations, are there one or two of these alternative methods that you have found particularly worthwhile to try in situations where Newton's method doesn't perform well? Thanks!

* Alternative root-finding methods include bisection, secant, regula falsi, Halley's, Broyden's, fixed point iteration, Steffenson's, Ridder's, Brent's, Muller's, Bairstow's, Durand-Kerner, and more...!

[lrdheat]

(09-23-2023 06:40 PM)Eddie W. Shore Wrote:  My favorite addition is the ability to access two functions f(x) and g(x) from anywhere.

The store button/function needs to come back. And the multistate colon.

Agree! I do like this calculator, despite it’s quirks.

[carey]

(09-23-2023 02:20 PM)klesl Wrote:  A small modification of procedure written above
7) Click EXE again to update the value of f(x) and obtain the 2nd iterate: 0.5452392119
8) recall f() and insert ans, so you get f(ans) and press OK or EXE several times
the final result is 0,567143xxxx

After playing around with your great suggestion a little more, the entire procedure can be streamlined to avoid even using the x variable. Instead, after f(x) and g(x) functions are created, the initial guess (0.5) is entered in the Calculate screen so Ans becomes the initial guess. After that, your suggestion to create f(Ans) and repeatedly press EXE, gives each iterate.

The entire streamlined procedure is as follows:
1) From Home, highlight Calculate, click EXE and click Function.
2) Highlight Define f(x), enter e^-x, and click EXE.
3) Click Function, highlight Define g(x), click EXE, click x, and click EXE.
4) Enter 0.5, then click EXE.
5) Click Function, highlight f(x) and complete "f(" by clicking Ans and entering ")" to get "f(Ans)", select EXE and the first iterate 0.6065306597 is displayed.
6) To manually obtain subsequent iterates, click EXE repeatedly.

[Csaba Tizedes]

(09-23-2023 06:45 PM)carey Wrote:  These videos are great -- very nicely done! Thank you for sharing them!

are there one or two of these alternative methods that you have found particularly worthwhile to try in situations where Newton's method doesn't perform well? Thanks!

Thank you, unfortunately my (spoken and written) English really terrible, so you can enjoy them in Hungarian, if you check these:

CASIO fx-991CEX - a leghatékonyabb Classwiz Akcióban | CASIO fx-991CEX - the most powerful Classwiz in ACTION: https://www.youtube.com/playlist?list=PL...ons3wS2cef

Or these:
CASIO Classwiz (fx-991EX, 991DEX, 991CEX, fx-92+ Spéciale Collége or *ANY* models): https://www.youtube.com/playlist?list=PL...qJUMxqyeP2

BTW I prefer the built-in solver, I have no other preferred method, in these videos I choosed Newton's method, because easy to implement on 991CW.

If you want to see something tricky, try this bisection in spreadsheet, but you can use the definition f(x) on 991CW:

[carey]

Csaba,
Thanks for your reply and for these great links!
Carey

[Quadratica]

It has the cross product of two vectors, whereas the 991EX didn't. I also like the fact that all the memory variables can be seen at once. There isn't a calculator which has some minor irritations so on the whole I prefer the 991CW to the 991EX. I use it more than my PRIME and TI CAS.

[Csaba Tizedes]

A.) It has the cross product of two vectors, whereas the 991EX didn't.
Simple use product (X) key

B.) all the memory variables can be seen at once.
thats why RECALL is there

C.) some minor irritations
IMHO best joke of 2023

Cs.

[Quadratica]

(09-26-2023 04:54 PM)Csaba Tizedes Wrote:  A.) It has the cross product of two vectors, whereas the 991EX didn't.
Simple use product (X) key

B.) all the memory variables can be seen at once.
thats why RECALL is there

C.) some minor irritations
IMHO best joke of 2023

Cs.

Thanks Csaba: That's what I mean, I had no idea that the cross product can be done on the EX because it isn't in the vector menu, whereas the dot product is. Every calc has its foibles.

[Csaba Tizedes]

A new brainf... - try it on your new gadget, I guess CW same as (C)EX in this field:

A review of built-in equation solver: How to use SOLVE on Elliptic integrals and Separable diffeqs - and many more example.





PDF version here:
PDF VERSION GOOGLE DRIVE

Cs.

[Matt Agajanian]

See this header pict of a Casio FB page. It shows that the 991CW is the upgrade from the 991ES Plus 2nd Edition. I know, it could've been a Photoshop job. But it does bring up an amusing idea. What do you think?

Casio Calculator.bd

[klesl]

I understand the picture it is time to upgrade from 991es plus 2nd edition to 991cw- go for better model:-)

[Matt Agajanian]

(12-08-2023 08:46 AM)klesl Wrote:  I understand the picture it is time to upgrade from 991es plus 2nd edition to 991cw- go for better model:-)

And you agree 991EX Classwix —> 991CW isn’t an ideal upgrade step. Right?