We consider some questions and the problems supplementing a basic course of the mathematical analysis at technical: calculation of Poisson integral by methods of integral calculus of functions of one variable, different approaches to calculation of volume of a ball in multidimensional space, various rare proofs of divergence of a harmonic series, calculation of the sums of Dirichlet series by means of infinite product. In popular textbooks these questions aren't considered as a rule. This material can be useful to teachers and well advanced students, facultative work, and preparation for the Olympic Games on mathematics etc.