Tadesse AbdiLechisa Gashew2025-08-182025-08-182024-06https://etd.aau.edu.et/handle/123456789/6985In this thesis, the construction of Green's function for IVP and BVP is discussed. We established continuity and symmetric properties of Green's function for ODEs, especially for Sturm-Liouville problems. We demonstrated the method of Green's function in conjunction with the Fourier transform to solve PDEs.en-USMethod of Green'sFunctionsThesis