Ecuaciones integrales de Fredholm y sus aplicaciones para los estudiantes de la carrera de Matemática de la ESPOCH

Abstract

The aim of this research project was to create a referential document to be used as a guide for the understanding of theoretical foundations in Fredholm integral equations, to discuss and extend the topics studied in the Functional Analysis courses in the Mathematics Major at Escuela Superior Politécnica de Chimborazo. For the development of the study, a documentary-type research with a qualitative approach and descriptive level was considered, the gathering and analysis of information was structured in a sequential way, by means of a documentary search process, identification, collection and selection of texts and articles available in reliable sources related to the proposed topic. The result obtained was a monograph entitled: "Fredholm integral equations and their applications", which is structured in four chapters where definitions and concepts such as bounded operator, symmetric kernel, integral operator, eigenfunction, among others, are described in a clear and understandable way. In addition, methods for solving linear and nonlinear Fredholm integral equations are also presented, as well as their application in the Sturm-Liouville problem, taut string with stable loads, among others. It is concluded that the monograph will help new and current students of Mathematics to understand and broaden their knowledge about integral equations to interpret situations involving this type of equations, as well as their resolution. Finally, it is recommended to broaden this research, in order to carry out a detailed study on Volterra’s integral equations.