Green's function for regular and singular boundary-value problems

This thesis seeks to find the Green's functions for a singular boundary-value problem, by first transforming the singular problems into a regular one, and then find the Green's function of the regular problem, which directly yields the Green's function of the original singular problem. In this thesis, a five steps procedure will be used as a general method to get the singular Green's function. Lastly, we illustrate our method by constructing the Green's function of a simple singular Legendre problem.