Bahru TsegayeChali Bekele2025-09-122025-09-122024-09https://etd.aau.edu.et/handle/123456789/7439The aim of this paper is to present a new definition of the Green function of the Dirichlet problem for the Laplace equation prompted by the theory of ordinary Differential equation and Partial Differential Equations. A Green function, a mathematical function that was introduced by George Green in 1793-1841. Green function use for solving Ordinary and Partial differential equations in different dimensions for both time dependent and time independent problems. Green function is used in many theories such as quantum field theory, Electrodynamics and statistical field theory to refer various types of functionsen-USLaplace’s EquationPoisson EquationFundamental SolutionGreen’s FunctionGreen’s TheoremGreen’s IdentitiesGreen’s PropertiesDirichlet Boundary Conditions.Thesis