[maweaver]

> What can we expect students to get out of an elementary course in differential equations? I reject the “bag of tricks” answer to this question. A course taught as a bag of tricks is devoid of educational value. One year later, the students will forget the tricks, most of which are useless anyway.

That's exactly how I was taught differential equations 20 years ago. And as expected I have totally forgotten all of them. I do wish I'd gotten some deeper lessons from it. Even a concept or two that stuck with me would be better than remembering I learned a bunch of math tricks a long time ago that I can no longer do.

[mrkeen]

The further I got into maths (not very far mind you, but I think I at least did a few differential equations,) the more it felt that maths really was just a bag of tricks, moreso at the advanced end.

* Keep deriving circular functions until they cancel out. * Completing the square * Use the quadratic formula to solve degree-2 polynomials ... No formula for degree-5 or higher. * Use the Laplace transform here... for reasons...

[ducttapecrown]

Many famous mathematicians have quotes along the lines of "it's not the result that mattered here, it's the new method/trick that is cool!" and essentially it's because solving math problems requires a bag of tricks and a new one can open new doors in every field it hasn't been applied to yet.

[BeetleB]

How often have you used them. It's been decades for me as well, but I still remember how to solve basic linear differential equations as I needed to use them often (in other courses).