Green's function for finitely many intervals Sturm-Liouville problems

The Green's function has been constructed for one-interval and two-interval Sturm-Liouville problems in which the discontinuity of its derivative is not determined beforehand but occurs on its own. This thesis seeks to extend that idea and construct the Green's function for finitely many intervals case. We consider the second order scalar differential equation with its boundary conditions and convert it to its equivalent first order linear system. From this conversion, we formulate the characteristic function whose zeroes are the eigenvalues of the homogeneous system. In addition, we construct the generalized matrix Green's function from which we get the top right component as the Green's function for finitely many intervals Sturm-Liouville problems.