Fourier series - Partial Differential Equations

One more application of series arises in the study of Partial Differential Equations.  One of the more generally employed methods in that subject use Fourier Series. Several applications of series, particularly those in the differential equations fields, rely on the fact that functions can be presented like a series.  In these types of applications it is very hard, if not impossible, to find out the function itself. Though, there are methods of determining the series representation for the not known function.