الفهرس 
Chapter 1: Mathematical PreliminaryOnly 14 pages are availabe for public view
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Abstract
This M.Sc. thesis entitled “Double approximate solution of the second kind Fredholm integral equation using orthogonal polynomials’’ was prepared by Eng. Mariam Morgan Kamel Morgan, Teaching Assistant at the Department of Engineering Physics and Mathematics, Faculty of Engineering and Technology, German University in Egypt. Under the Supervision of Prof. Dr. Said Elserafi and Dr. Hany Ahmed Attia El Gohary, at the Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Egypt. The aim of this thesis is focused on the numerical solutions of Fredholm integral equations of the second kind. Presented two new computational methods based on a new established method of Legendre Interpolation Polynomials. For the two methods the Legendre polynomials is modified in the form of matrices and applied for the unknown function, the given data function and the kernel by using different techniques that suitable the idea of each method. from the computational results, it illustrative that the two presented methods with exact solutions, clearly simplify the computations, reducing the round-off errors, saving time and ensure the superiority of these methods compared with errors.