Is tex file available? Isn't this a difference equation that can't be converted to a differential equation?

Hi, I had a few questions -- and I apologize for my ignorance, since I am new here!

- Are the LaTeX files available for this or any of the other resources on Simiode? I would love to be able to customize the tasks.
- The M&M problem results in a finite difference equation that can be solved as a recurrence relation. But you get a different (and a little bit wrong) answer using the differential equation approach. Is this just a point of discussion you usually have with students?
- Is there an "answer key" for this or any of the other resources on Simiode?

Thank you for your help and advice!

John Chase

Rockville MD

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Brian Winkel@ onHi John,

Permit me to answer your questions in public and then drop you a note of encouragement/engagement in email.

First, we are migrating all SIMIODE resources from our own Hub at www.simiode.org where you are finding us and our resources to https://qubeshub.org/community/groups/simiode where you can join free and identify yourself as Instructor to access all teaching materials. We are still straddling both environments and hope to do this in a few months - it has been too long in finishing!

Second, and beyond to your questions. . .

1. Are the LaTeX files available for this or any of the other resources on Simiode? I would love to be able to customize the tasks.

Most SIMIODE Modeling Scenarios are written in LaTeX and when you are identified as Teacher in the old setting (here) or Instructor in the new setting in QUBES you have access to the .tex files and we encourage you to download, modify customize, jazz up, tone down, perhaps even publish in SIMIODE a variant or different strategic approach. The Student and Teacher versions in this case just have a toggle and unfortunately the .tex Student versions have all the materials (answers, strategies, and the like) that the Teacher Version has. Gotta re-edit all of these in our new home in QUBES. Those that are written in WORD have both the pdf and doc version available for the same purpose.

2. The M&M problem results in a finite difference equation that can be solved as a recurrence relation. But you get a different (and a little bit wrong) answer using the differential equation approach. Is this just a point of discussion you usually have with students?

Yes the initial model for the m&m is a difference equation, because it is a discrete process, VERY much so, "one, two, three, etc." But what we want to do in the first class which is where this material is often used is get lots of vocabulary in for future reference, such as equilibrium value or stability, and show the transition between difference and differential equations, yes with some loss of reality in going each way, but capturing the essence in both cases. It would be good if you would point out the "little bit wrong" for further discussion, please.

3. Is there an "answer key" for this or any of the other resources on Simiode?

All Modeling Scenarios have a Teacher Version and at the end of the material offered in the Student Version you can see a section labeled "COMMENTS" or "NOTES TO THE TEACHER" in which the author(s) describe issues, solutions, strategies, jumping off points, collegial sharing, etc. Further we have opportunities for folks to make COMMENTS as you are doing on the material itself and we really encourage that, although few exercise this engagement prospect. So we are very grateful to hear from you in this manner.

Take care and be well. Enjoy modeling to motivate learning differential equations. Thank you for taking the time to comment.

Brian Winkel, Director SIMIODE, BrianWinkel@simiode.org

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