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    Fourier Series of a Periodic Fuction : Convergence

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    Work out the Fourier series of f, given over one period as follows.
    At which values of x does the series fail to converge to f(x)? To what values does it converge at those points?

    (h) |cos x| for all x
    (k) x on 0<x<1, 1<x<2.

    See the attached file.

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    Please see the attached file for the complete solution.

    Solution. By a theorem which states, if y=f(x) is a periodic function and y=f(x) is continuous at x=a, then its Fouries series converges to x=a; if y=f(x) is NOT continuous at x=b, then its Fouries series fails to converge to x=b. So,

    (a) Its Fourier series converges to all points in and ...

    Solution Summary

    Convergence of Fourier Series of Periodic Fuctions is investigated. The solution is detailed and well presented.