The document discusses Fourier series and their application to functions defined over intervals. It defines the Fourier sine and cosine series for functions on [-L,L] by extending the functions to the full interval [-π,π] in an odd or even way. The Fourier sine series results from the odd extension, using sine terms, while the Fourier cosine series uses the even extension and cosine terms. Examples are provided of calculating the Fourier sine and cosine series for basic functions over [-1,1]. The approach generalizes to 2L-periodic functions defined on [-L,L].