Question

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

Answer 1

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.

Answer 2

So, then I should be using the Complex Fourier Series for most of the problems?

Answer 3

Yeah, that's how I'd go about doing it. Decompose to other representations such as cosine or sine when you have to.