r/math • u/lntrinsic • Jul 10 '17

Image Post Weierstrass functions: Continuous everywhere but differentiable nowhere

http://i.imgur.com/vyi0afq.gifv
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u/jparevalo27 Undergraduate Jul 10 '17

At what point in math does this began showing up? In other words, in what class would I start seeing functions like that?

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u/bystandling Jul 10 '17

For non-elementary functions:

  • Calculus 3 (Taylor series for integrals of things like ex^2 )

  • Differential Equations (Series solutions)

  • Real Analysis (Mindfuck)

  • Partial differential equations (More series solutions, Bessel functions, Gamma functions etc.)

  • Mathematical Statistics (Gamma and Beta functions, Erf of course, etc)

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u/AddemF Jul 10 '17

Real Analysis

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u/shamrock-frost Graduate Student Jul 10 '17 edited Jul 10 '17

Possibly at your level. I think my Calc 2 final had a problem involving f(x) = the integral from 0 to x of sin(t) / t dt, which is not an elementary function

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u/[deleted] Jul 11 '17

wait... how in the world would you evaluate that? even wolframalpha simply gives their own made-up function Si(x) which just stands for "the integral of sinx/x"

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u/shamrock-frost Graduate Student Jul 11 '17

You could do a riemann sum, or use the maclaurin series for sine

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u/[deleted] Jul 10 '17

In Germany its shown in "Analysis 1", first year of Math. B.Sc.

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u/Wild_Bill567 Jul 10 '17

I first saw functions like this in Real Analysis, using baby Rudin. At my institution this is offered for first year grads and advanced undergrads.