Fourier Series: Part (2)pic.twitter.com/M4wvRCl6VF
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There are a couple refining points I'd like to make. (1) "any function f(x)" means any function f(x) satisfying the so-called "Dirichlet conditions". However, these conditions are really, really quite general.
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(2) In equations (3) and (4) you will notice I replaced an equality that had the index "m" with an equality which had the index "n". This is permitted, since the relation was shown for all m, hence it's also true for m=n.
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(3) Example: If f(x) is a square wave, then the result looks like this. As you can see, the more terms we keep in the series, the better the square wave is approximated by the the Fourier Series.pic.twitter.com/i2FXLmIYDy
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