Effective methods of uniform approximations based on the polynomas of Chebyshev

The work discusses the issues of approximation of functions, methods for calculating certain integrals, close solutions for the integrated equations of Fredgolm and Voltaire of the second kind, operator equations, the equations of Fredgolm of the first kind and some singular integral equations. All approximate decisions are based on the calculation of asymptotic polynomials, which are described using the Polynomas of Chebyshev of the first and second kind. A direction based on the use of asymptotic polynomials for uniform approximation of functions allows you to represent the function, both in algebraic and in trigonometric form, and are polynomial to consider both asymptotic and interpolation. The uniqueness of asymptotic polynomials consists in a very convenient form of presentation of the error of their approach in the form of the decomposition of the residual member in a row of Fury-Chebyshev. This allows you to choose the degree of polynomial that approximates the desired function with pre -given accuracy.
The work is intended for students, graduate students and everyone who is engaged in uniform approaches of the tasks considered