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I'm trying to plot partial sum of Fourier series. I've finally managed to make it work but there are several things I don't understand

f = Piecewise[{{Mod[x, Pi], Mod[x, 2 Pi] < Pi}, {Mod[-x, Pi], Mod[x, 2 Pi] >= Pi}}]
g = FourierSeries[f, x, 2]
Plot[{g, f}, {x, -10, 10}]

enter image description here

My questions are :

  1. Why does it stop working when I directly put the value of g in Plot (only f is plotted) ?

    f = Piecewise[{{Mod[x, Pi], Mod[x, 2 Pi] < Pi}, {Mod[-x, Pi],Mod[x, 2 Pi]>= Pi}}]
    Plot[{FourierSeries[f, x, 2], f}, {x, -10, 10}]
    
  2. Why does it stop working when I define g like this (only f is plotted)?

    g[x_] := FourierSeries[f, x, 2]
    Plot[{g[x], f}, {x, -10, 10}]
    
  3. I also tried to add a slider to set the number terms to add. It seems to work but it makes Mathematica freeze...

    f = Piecewise[{{Mod[x, Pi], Mod[x, 2 Pi] < Pi}, {Mod[-x, Pi],Mod[x, 2 Pi] >= Pi}}]
    Slider[Dynamic[n], {1, 10, 1}]
    Dynamic[g = FourierSeries[f, x, n]]
    Dynamic[Plot[{g, f}, {x, -10, 10}]]
    

Thanks :) !

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  • $\begingroup$ Re 1: Because x is set to a numeric value before the series is computed. Re 2: Ditto; use g[x_?NumericQ] := FourierSeries[f, x, 2]. Re 3: Totally different. You get into a Dynamic infinite loop because setting g causes another update. Try Dynamic[g = FourierSeries[f, x, n], TrackedSymbols :> {n}]. $\endgroup$ – Michael E2 Nov 21 '15 at 18:05
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I guess I can put my comment in an answer:

  • Re 1: Because x is set to a numeric value before the series is computed.
  • Re 2: Ditto; use g[x_?NumericQ] := FourierSeries[f, x, 2].
  • Re 3: Totally different. You get into a Dynamic infinite loop because setting g causes another update. Try Dynamic[g = FourierSeries[f, x, n], TrackedSymbols :> {n}].

The first two questions are more or less a duplicate of What are the most common pitfalls awaiting new users?

The third question comes up in so many forms, it's hard to find an exact duplicate. The underlying issue in Can Table be used inside Manipulate? is the same, although it's a rather complicated example compared to this one.

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  • $\begingroup$ Thanks ! I learned a lot from those two links ! $\endgroup$ – user2737248 Nov 22 '15 at 10:39

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