The coefficients for a Fourier Series can be determined using the Fourier coefficients formula, which involves integrating the function over one period and dividing by the period. This process is repeated for each term in the series.
Yes, as long as the function is periodic and has a finite number of discontinuities, a Fourier Series can be written for it. The series may not converge to the original function at the points of discontinuity, but it will still be a valid representation of the function over the given interval.
An open interval means that the function is periodic, but not continuous at the endpoints of the interval. In this case, the Fourier Series will use only sine or cosine terms. A closed interval means the function is both periodic and continuous at the endpoints, allowing for a full representation using both sine and cosine terms.
Yes, if the function is odd or even, the Fourier Series will have a simplified form with only sine or cosine terms, respectively. Additionally, if the function is symmetric about the midpoint of the interval, the Fourier Series will only have cosine terms.
No, a Fourier Series is only applicable for periodic functions. For non-periodic functions, other methods such as Taylor series or numerical integration may be used for approximation.