Calculus Programs - LRAM, RRAM, MRAM

[Sean Bird]

I recently responded to a question about programs on the TI-Nspire that perhaps others would find helpful...

RAM= Riemann Approximation Methods are popular tools to explore definite integrals in many text books. I used to use programs for the 83/84 and 89. One trick was when the book said to find the result for 100 subintervals, it would take those devices a long time to churn out the result. With the TI-Nspire, I'm not afraid if the students try larger numbers to see what happens as they use more and more rectangles to approximate the integral.

LRAM, RRAM, MRAM (left, right, midpoint Riemann Approximation Method for definite integrals) are able to be explored using programs I wrote for the TI-Nspire or TI-Nspire CAS when it first came out and have improved as the TI-Nspire improved. (Perhaps this next week I'll make another little improvement to ram( ), especially if we have another snow day.)

The 'area' file is available on our TI-Nspire Google Group Website:
area.tns Download "Riemann programs for your library. RAM, LRAM, trap and all that. Improved." 

This file is cited with the "Sum Rectangles" activity that appeared on TI-math.

SumRectangles.tns Download

Colorful activity with extension Script app. Coming to TImath.com

49k

v. 7

Oct 29, 2012, 5:37 PM

The above links have the latest version of those files, but they are also available on education.ti.com Activities Exchange 

Here was a little video I put together to explain a bit about libraries and using the area.tns as the example.
http://www.youtube.com/watch?v=yPCedUZgRvU

More can be said about the limited value (great for exploring and discovering and sometimes for checking work) of the programs - like they only work when you have a function. The approximation tools are often used when you don't have a function, but only have data. The Vernier DataQuest application has some nice possibilities for actual data and graphically seeing trapezoids.

The Math Nspired activities certainly have some lovely features -
http://education.ti.com/en/timathnspired/us/calculus/definite-integrals-and-applications

- but the program and files cited at beginning of this email allow for increased flexibility of the functions that can be explored and the number of subintervals.

The Riemann Sums activity on Math Nspired has been optimized for the iPad app too.

Enjoy,

Sean Bird

[Ray Fox]

Congratulations on being elected to the TI board. You are definitely the right choice. I was delighted to see your nominationand voted for you.

Ray

On Saturday, February 1, 2014, Sean Bird <covena...@gmail.com> wrote:

I recently responded to a question about programs on the TI-Nspire that perhaps others would find helpful...

RAM= Riemann Approximation Methods are popular tools to explore definite integrals in many text books. I used to use programs for the 83/84 and 89. One trick was when the book said to find the result for 100 subintervals, it would take those devices a long time to churn out the result. With the TI-Nspire, I'm not afraid if the students try larger numbers to see what happens as they use more and more rectangles to approximate the integral.

LRAM, RRAM, MRAM (left, right, midpoint Riemann Approximation Method for definite integrals) are able to be explored using programs I wrote for the TI-Nspire or TI-Nspire CAS when it first came out and have improved as the TI-Nspire improved. (Perhaps this next week I'll make another little improvement to ram( ), especially if we have another snow day.)

The 'area' file is available on our TI-Nspire Google Group Website:
area.tns Download "Riemann programs for your library. RAM, LRAM, trap and all that. Improved." 

This file is cited with the "Sum Rectangles" activity that appeared on TI-math.

SumRectangles.tns Download

Colorful activity with extension Script app. Coming to TImath.com

49k

v. 7

Oct 29, 2012, 5:37 PM

The above links have the latest version of those files, but they are also available on education.ti.com Activities Exchange 

Here was a little video I put together to explain a bit about libraries and using the area.tns as the example.

TI-Nspire Tips Library ram integral program

More can be said about the limited value (great for exploring and discovering and sometimes for checking work) of the programs - like they only work when you have a function. The approximation tools are often used when you don't have a function, but only have data. The Vernier DataQuest application has some nice possibilities for actual data and graphically seeing trapezoids.

The Math Nspired activities certainly have some lovely features -
http://education.ti.com/en/timathnspired/us/calculus/definite-integrals-and-applications

- but the program and files cited at beginning of this email allow for increased flexibility of the functions that can be explored and the number of subintervals.

The Riemann Sums activity on Math Nspired has been optimized for the iPad app too.

Enjoy,

Sean Bird

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[TRMP]

Hi Sean, is it possible to download all files, at once, from TI-Nspire Google Group Website ?

Thanks...

[Sean Bird]

With the browser Firefox I have used Download Them All
https://addons.mozilla.org/en-US/firefox/addon/downthemall/

[TRMP]

DONE. TY

Em sábado, 1 de fevereiro de 2014 10h16min25s UTC-2, Bird escreveu:

[Sean Bird]

We did have another snow day, so as hoped for, an improved version of the program in now up on our Google Website.  area.tns "Riemann programs for your library. RAM, LRAM, trap and all that. Improved."

Fonts are fixed and

ram() now does trapezoids and tells you if the Simpson's rule isn't suppose to work because n is odd.

Enjoy,
Sean Bird

[John Hanna]

Very nice, Sean.

One small suggestion: include the function definition in the output.

 

Enjoy the snow,

     John Hanna

     jeh...@optonline.net

     www.johnhanna.us

     T³ - Teachers Teaching with Technology

     "the future isn't what it used to be."

 

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[Sean Bird]

Oh, the benefits of collaboration! With that suggestion form John, a couple of improvement have been made.

area.tns is still posted at the same location. Last night I uploaded updates to the program ram() that included showing the function on the output and allowing the student to request the number of decimals to show - the default is 3.

I actually haven't tested it on a numeric Nspire, so if someone could do that, it would be appreciated. My only concern is with showing the function.

If you want an exact solutions try the program rs(b,a,n) when f1(x) is defined either on a graph, calculator, or notes page.

- Sean Bird

[John Hart]

Dear Mr. Bird,

I have recently downloaded the latest version of the Area program and have followed all the steps in the video to try and get a RAM integral program on my TI-Nspire CX (not CAS). I have followed all the steps in the video, and have successfully added the program to MyLib, but unfortunately, when I try to do the RAM program, it comes up with the error "Variable not Defined". I left the a comment on the video and was recommended to join this group so I can attach the file I am using. Thank you for all your help,

John Hart

[Sean Bird]

Thanks for the screen captures and the attached file. I'll look into this.

[Sean Bird]

I tried it out but couldn't get the error. Currently I don't have the numeric TI-Nspire installed on my computer or have one with me.

After looking at the program I have a theory and a solution (it that is what the problem is).

Perhaps the problem is the line of code that says
Define f(x)=f1(x)
Request "f(x) =",f(x)

The reason I included this is so that if you had already graphed the function in f1(x), you would not need to retype it again in "2D, non-pretty or math print", e.g. f(x) = x^2/3. If you had already entered that in f1(x), you wouldn't need to do type it in incorrectly.

I would recommend either, 1st define f1(x) by graphing it or on a Calculator page Menu > Action > Define or use f1(x):=

If you don't like to do that (or that doesn't solve the problem), then try deleting the line "Define f(x)=f1(x)"

You'll need to save the area.tns and Refresh your Library.

If my expert programming friends see something else, I welcome your thoughts.

Thanks all.

[John Hart]

Mr. Bird,

I tried all of the solutions that I think you said (to the best of my ability), and ended up with different errors. I will attach screenshots of what I did to this message. I originally tried graphing and then using f1(x) to skip the 2d math print, and that was the variable not defined, and the same thing would happen when I Defined f1(x) = sin(x).  so I then tried  Define f(x) = sin(x) and then just plugged in f(x) = f(x) into the pop up box, but i got the error "Resource Exhaustion." So I then deleted the code that you told me to delete, and plugged in sin(x) into the pop up box, and it gave me the error that only numerical values could be imputed. I don't know why this is such a struggle for my calculator when it works for other people, so thank you for helping me through this.

John Hart

[Sean Bird]

Appreciate your efforts. (Can others help who have numeric Nspire or numeric Nspire and programming knowledge)

Have you tried the other programs that aren't as fancy?

You need to define f1(x)

then in the parentheses of the program you give your values for b, a, and n. For example rs(5,1,8)

I may be able to try it with a numeric handheld at school today.

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Sean Bird
Covenant Christian High School
Psalm 111:2 “Great are the works of the LORD, studied by all who delight in them.”

[Dennis Donovan]

Sean,

The problem is not defining f(x) it is in the Text command at the end when you try to display the function, just delete the "f(x)="&string(f(x)& part of the text command and it works.

Dennis

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From: Sean Bird <covena...@gmail.com>
To: tinspire <tins...@googlegroups.com>
Sent: Thursday, December 1, 2016 7:19 AM
Subject: Re: [tinspire] Re: Calculus Programs - LRAM, RRAM, MRAM

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[Dennis Donovan]

To further elaborate.

f and f1 are defined on the variable list on the numeric, but when you type f(x) on the calc page you get the same error, f(2) works fine.  Same for f1, which is defined, but f1(x) on the calc page results in this same error.

I know that you can't do algebraic manipulation on the numeric, but I would think you could at least display the function definition.

I think that the error message is that x is not defined, not that f or f1 are not defined, but that is just a guess.

Dennis

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From: Sean Bird <covena...@gmail.com>
To: tinspire <tins...@googlegroups.com>
Sent: Thursday, December 1, 2016 7:19 AM
Subject: Re: [tinspire] Re: Calculus Programs - LRAM, RRAM, MRAM

[Sean Bird]

Could you attached your version of the area.tns?

Thanks.

I was thinking about something with strings would fix it. Yes, the numeric does great with f(a number), but it won't give what f(variable) is on a calculator page.

[Dennis Donovan]

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From: Sean Bird <covena...@gmail.com>
To: tinspire <tins...@googlegroups.com>

Sent: Thursday, December 1, 2016 7:51 AM