On the Use of Green's Functions in Solving Boundary Value Problems

There is no doubt that Green's functions have a long history in their use in many fields of applied mathematics and physics and especially in solving boundary value problems, hence we thought that it is worthwhile to write this article to summarize some important results in this concern emphasizing the beauty behind using them and the elegant mathematical techniques used as tools in conjunction with them. Famous problems relate to wave propagation and potential theory will be tackled in some details, giving the solutions of the partial differential equation which are connected with the problem. There remains also tomention that Green's functions are used in many other applications as will be pointed out in the conclusions