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Showing My Students Both the Rough and Paved Paths, And Letting Them Choose

Student "edition" found at {csi dot journalspace dot com}.

Maybe I shouldn't have started this blog now, not with everything that's been going on.

Day 4, Week 6, Term 1, Differential Equations class. I continued with the example I started writing down during the last meeting. Technically I wrote down the entire solution in the previous session, but I chose an alternate method of solving not previously introduced (but used in the textbook) because it was supposed to be a longer, more difficult extrapolation.

This time I set to prove how complicated it was. The integration, to be broken down into easy to convert expressions, had to be subjected to the partial fractions equivalents, something I was sure they had learned but probably dismissed as a one-time application during their formative math years.

I got through the most intricate hurdle, then I assigned it to them as a bonus if they could complete the solution and make the same final answer come up as the “easy” method reached.

I went through two more examples, and had to endure patiently as the same questions about basic steps cropped up again and again, and that they really learned and were adamant on learning through their questions. My only consolation is that Deiv was not in that class to add further repetitive questions.

Just to be sure that they did understand the procedure, I gave them homework, teasing them by asking one of their classmates to come up with a number from one to ten. When she said “eight”, I said there would be that many items in their assignment. But I really just gave them three questions.

In the Introduction to Electricity and Magnetism lecture class afterwards I continued with the symmetries of imaginary Gaussian enclosures, this time going into spherical surface symmetry for a hollow charged spherical shell.

I prided myself in being able to draw clearly a cut away view of a hollow shell, just like those pictures showing the layers of a planet. Then I compared it to a particle of the same charge and the same Gaussian surface, with no difference in the flux computed.

For inside such a shell, I also illustrated that the electric field inside is equal to zero because there is no charge enclosed.

Lastly for cylindrical surface symmetry I showed concentric hollow charged cubes and the field inside the inner tube (nonexistent) between the tubes and outside both tubes.

Afterwards it was just a couple of examples on all the types of symmetries that I gave.

The road session 634 is on leads to a dead end here. For now, class dismissed.


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