Analysis and aplications of Fredholm integral equations of the second kinds

This thesis aims to shed light on the basic issues in this field by examining integral equations and their types in detail. Integral equations have an important role in mathematical modeling and analysis of physical systems. In this study, the general structure of integral equations, various solution methods and applications are discussed. In the first part of the study, information is given about the history of integral equations and the studies carried out to date. In the second part of the study, an overview of the basic concepts of integral equations is presented. In the third part, these equations are analyzed according to different properties. It is classified and explained. In the fourth chapter, the relationship between differential equations and integral equations is explained and the methods for converting the min to each other are given. In the fifth chapter, Fredholm integral equations are discussed and definitions and terms regarding their having a single solution are given. These theorems are supported with examples. In the sixth chapter, solution methods of Fredholm integral equations are mentioned and applications of these methods are given.