M.Sc.

The main purpose of this work may be divided into the following aspects: 1. Study the Chebyshev polynomials of the first and second kinds defined on the intervals [0,1] and [-1,1] and modify some of their properties. 2. Use two methods to solve the linear ordinary differential equations with nonconstant coefficients, namely, Chebyshev-matrix method and Chebyshev series method. 3. Devote Chebyshev series method to solve system of linear Fredholm integral equations and integro-differential equations.

The main aim of this work is focused on studying the global asymptotic