I could never write a textbook on differential equations because every few pages I would digress into a long rant about how…

regexkind:

regexkind:

I could never write a textbook on differential equations because every few pages I would digress into a long rant about how insisting on only solving DEs with solutions in the family of elementary equations and steering clear of numerical methods is a sign that you are some sort of quisling for the Supreme Fascist, who has vouchsafed us these little crumbs, and that any proud person should be unafraid of getting their hands dirty, and what I would do to G-d if he ever comes back around here again, etc etc,

basicallyaturtle tags: #i think the thing about analytically solvable DEs is that it is a puzzle to be solved #it on occasion is very fun to have a problem that you need to solve and know it can be done and justbhave to find thebwaybto do that #series solutions can be part of thatnpuzzle #but on generally they're just a lot messier and not as satisfying because of course the DE has a series solution #(not literally of course #plenty do not have series solutions) #but yes in working with dE's outside of a DE class perspective one must on the face of it #accept that computational methods are essentialALT

This is a balanced viewpoint and I respect it but I still feel like this is conceding too much ground to those who teach DEs as though the toolkit of fun puzzles is all there is. I don’t think we should “accept”. I think we should embrace. I think we should spend more time on error bounds, not just because they are necessary, but because the mathematical fields devoted to building approximations which behave nicely have their own beauty