The textbook describes the basics of numerical methods for solving problems of mathematical analysis, linear algebra and ordinary differential equations. Considerable attention is paid to the issues of algorithmization of methods. It can be used when performing laboratory, course, final qualification and research works. Each topic contains a theoretical justification and a large number of examples of solving practical problems using the Maple mathematical package. Meets the requirements of the federal state educational standards of higher education of the latest generation. It is intended for students, postgraduates, university teachers, as well as for engineers and researchers who use numerical methods to solve applied problems.