Partial linear differential operators and construction of their green's function

In this thesis, the problem of the construction of Green?s function of partial lineer differential operators discussed, studied and learned. Especially, with the use of ?- function for the initial value of partial differential equations, boundary value problems were constructed. In this thesis, the function and the Fourier transform of ? - were shown. We constructed the Green?s functions of the boundary value and initial value problems for the wave equation and the heat equation. We used the Fourier series, Fourier transform and their propertions in these constructions. We found the solutions of each problem with the help of suitable Green?s functions.