Mathematical analysis. The function of one variable

The training manual in accordance with the work program of the Higher Mathematics discipline sets out the main provisions of mathematical analysis that meet the requirements for the main mandatory program for the training of certified specialists at a technical university.
The textbook is built in the form of consistent and closed lectures and sets of individual practical classes in order to increase the intensity of students" independent work. The manual consists of lectures on three topics, namely - the introduction to the analysis, derivative of both its applications and integral calculation of the function of one variable.
The manual contains carefully disassembled examples, geometric illustrations and applications. The issues of the technique of finding derivatives and the application of derivatives for the study of the behavior of functions, the approximate calculation of functions, the approximate calculation of the roots of the equations and much more are considered in detail. The issues of differential geometry on the plane and space are considered in sufficient detail. In addition, some rules of standard numerical methods of engineering calculations and the correct design of their answers are considered.
The issues of integral calculation of the function of one variable and its technical applications are considered. In detail, methods of taking indefinite, certain and non -unit integrals are described in detail. Applications of integral calculus to the tasks of geometry, theoretical mechanics and physics are given.
The manual includes questions for self -control and quite large in volume individual tasks (IPZ), the implementation of which occurs at practical seminars under the guidance of the teacher. In addition, home control tasks (IDZ) are given, having completed which students will be able to confidently learn this topic on their own. The textbook is intended primarily for the distance learning of students in absentia in absentee for technical universities in the development of the “Higher Mathematics” discipline, but it can also be useful for daytime learning students