#mathsToday #mtbos Slope fields in Desmos: Here's a simple graph that plots any slope field and, optionally, a solution func if one is known. I've resisted the impulse to add features, but it would be easy to do many things. www.desmos.com/geometry/ghy... - ThreadSky

tcorica.bsky.social • 113 days ago

#mathsToday #mtbos Slope fields in Desmos: Here's a simple graph that plots any slope field and, optionally, a solution func if one is known. I've resisted the impulse to add features, but it would be easy to do many things. https://www.desmos.com/geometry/ghy0vzw6ta

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tcorica.bsky.social•113 days ago

For example: https://www.desmos.com/geometry/nm050g8tyy

malmeida.bsky.social•113 days ago

I made one recently too: https://www.desmos.com/calculator/brvpwmucy9

tcorica.bsky.social•113 days ago

Nice! I chose Desmos/Geometry because I felt the segment command made more sense than the polygon command.

I tried to keep mine as simple as I could so that kids could understand all the moving parts. This was used as an intro/review preceding lessons on vector fields (in MVC).

richardtrimble.bsky.social•108 days ago

https://geogebra.github.io/docs/manual/en/commands/SlopeField/

You might find the slopefield tool on geogebra easier. Together with SolveODE or NSolveODE you can investigate a lot of differential equations

tcorica.bsky.social•108 days ago

Thank you. I think I prefer the Desmos approach for this particular case because (1) the bones are visible and tweakable to the kids and (2) my purpose here is to show the connection to vector fields, rather than to teach DEs per se. 1/2

tcorica.bsky.social•108 days ago

My preference for visible bones: in fact, we (MVC) do a day of Euler's Method using a *spreadsheet*, and then gradient descent using a ss. I've also done SIR model using a spreadsheet in BC Calc.

I'm always impressed with what Geogebra can do, of course! 2/2

richardtrimble.bsky.social•108 days ago

I guess you are teaching in the USA.

Sadly here in the UK we lost Euler's method from most syllabii in Secondary school in 2017. But, yes, I always started with spreadsheets too!

Great fun. Do you explore the error term being proportional to the square of the step size?

tcorica.bsky.social•108 days ago

"...error term": No, that's actually news to me! Not in our syllabi at all.

EM is required for BC Calc (not AB); I recap it in MVC as an intro to ∇Descent. BC≈Calc1; AB≈Calc2, MVC≈Calc3.

My bias is that numerical methods are even more important now, given the increase in computer power.

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