The textbook contains lecture material for the second part of the course on math-ematical analysis and includes the following topics: indefinite integral definite inte-gral and its geometric applications improper integral numerical series functional sequences and series power series Fourier series. A useful feature of the book is the possibility of studying the course material at the same time as viewing video lectures recorded by the author and available on youtube.com. Sections and subsections of the textbook are provided with information about the lecture number the start time of the corresponding fragment and the duration of this fragment. In the electronic version of the textbook this information is presented as hyperlinks allowing reader to immediately view the required fragment of the lecture. ьThe textbook is intended for students specializing in science and engineering.