Fourier Series of Piece-wise Smooth Functions
Our goal in this video is to prove the following:
If the function f(x) is ``piece-wise smooth,'' then its (complex) Fourier series converges uniformly to f(x).
Note that the condition in this theorem does not involve the Fourier coefficients; hence, it is more direct. Along the way, we also prove Bessel's inequality and Parseval's equality.
Lecture notes: https://bruneimathclub.blogspot.com/2...
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