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In PDE, how do we know to use Fourier Series, Cosine Fourier, Sine Fourier, or Complex Fourier Series?

Mathematics
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Well, they're mostly interchangeable. Fore example, the Complex Fourier Series is just a representation of Fourier Series as a whole and is composed of the sum of Cosine and Sine Series.
So, then I should be using the Complex Fourier Series for most of the problems?
Yeah, that's how I'd go about doing it. Decompose to other representations such as cosine or sine when you have to.

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