Lectures on the Theory of Numerical and Functional Series

The manual contains a systematic statement of four important sections of the general course of the mathematical analysis: the theory of numerical series, the theory of functional sequences and series, the theory of series of Fourier and the main data on Fourier’s integral. The statement is most approached to a lecture course.

The book is intended for bachelors which profoundly study mathematics.

Keywords: a series, sequence, convergence, uniform convergence, operations with convergent series, summation of divergent series, double and repeated series, infi nite products, power series, Fourier’s series on orthonormalized systems, Fourier’s trigonometrical series, Fourier’s integral