The present monograph has points in common with two branches of analysis. One of them is the variational-difference method (the finite element method), the other is the constructive theory of functions. The starting point is the construction of special classes of coordinate functions for the variational-difference method. It is based on elementary transformations .of the independent variables of given "primitive" functions. After the construction of the coordinate functions, the next step is to approximate functions of a given class by linear combinations of the coordinate functions, and to...