The textbook contains basic information on differential and integral calculus (functions, limits, derivatives, integrals, series), without which it is impossible to study both subsequent chapters of higher mathematics and general technical and special engineering disciplines. The material is presented in its original form, the author's methodological findings make it possible to simplify the presentation, make it more vivid and understandable. At the same time, the correspondence between rigor and simplicity of presentation is observed. Particular attention is paid to explaining the introduced mathematical concepts.