This manual is based on the course of lectures "Additional chapters of mathematics" , which have been read for many years by the author for students, Specialization in Theoretical Physics , The course on the choice of "Theory of symmetry" for third-year students and the course "Additional chapters of mathematics with applications" for undergraduates of the Faculty of Physics . The content of the lectures is mainly presented in the form of a brief summary; the topics on which laboratory tasks are performed are described in more detail . Tasks for each section are solved by students in practical classes and independently. In general, this manual is intended to help students in extracurricular work with recommended literature.