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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
16
votes
Taking "Zooming in on a point of a graph" seriously
I haven't seen any Calculus books take this approach. Possibly, this is because it is not clear how to proceed in the case of functions that are not polynomials. Consider even the really nice function …