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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
10
votes
Nonexistence of boundary between convergent and divergent series?
As Dylan Wilson pointed out, the following question appears in Folland's real analysis book:
(second edition, pg. 164) (33) There is no slowest rate of decay of the terms of an absolutely convergent …
6
votes
Interesting Calculus Questions/Exercises
The following problem is often found in introductory Real Analysis courses but can be solved by IVT:
Let $f :[0,1] \to [0,1]$ be continuous. Show that f(x) has a fixed point. In other words, there …