I no longer understand my PhD dissertation

Re:I no longer understand my PhD dissertation by sampo on Sunday February 14, 2016 @07:08PM (#11100687)

> Up through my first differential equations class I found almost everything trivial to learn

Mankind hasn't yet figured out a good way to teach the first Differential Equations course.

The first serious Calculus course introduces some level of rigor and formalism, but this alone is not sufficient for Diff Eqs. And the DE courses are typically leaning towards applications, so they tend to succumb to the "fiddle these dx's and dy's around like it's magic, in the end it might work out" approach.

The business is well founded, which you will discover later. But no one has figured out how to massage that into the first course.

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Re:I no longer understand my PhD dissertation by ghaff on Sunday February 14, 2016 @07:37PM (#11100792)

It's been a while but I think this is true of a lot of introductory courses in general, like Organic Chemistry. "Trust us and memorize these rules the basis of which will become clearer down the road."

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Re:I no longer understand my PhD dissertation by sampo on Sunday February 14, 2016 @09:50PM (#11101250)

This point is more thoroughly explained under section 7 here: https://web.williams.edu/Mathematics/lg5/Rota.pdf

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Re:I no longer understand my PhD dissertation by JabavuAdams on Sunday February 14, 2016 @11:10PM (#11101459)

Thanks for that. My engineering DiffEqs course is where my math foundation started to fail me.

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