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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

12 votes

What's a good introduction to category theory for someone doing analysis?

As requested, making comment into the answer. I think Helemskii's book "Lectures and Exercises on Functional Analysis" contains a very nice intro into category theory. It may be a bit light on the alg …
Anton Fetisov's user avatar
4 votes

Interesting Calculus Questions/Exercises

That's not really much of a problem, but still a nice stumbling block for inexperienced and an example of the evilness of formal symbol manipulations, even innocent-looking ones. Consider a function …