Abstract
Abstract : A formula yielding an expression for the Green's function of a linear separable elliptic partial differential equation in terms of the Green's function for two simpler equations, one of which is elliptic and the other hyperbolic, is derived utilizing separation of variables, transform techniques for solving ordinary differential equations, Parseval's identity from Fourier transform theory, and general properties of Green's and Riemann functions. The formula is applied successfully to specific problems, some of which are believed to be previously unsolved, and Green's functions are represented using the special functions of mathematical physics. A more detailed overview of the thesis may be found in Appendix A, which is the recommended starting point for reading this thesis. (Author)
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