Mathematical Analysis. Differentiation of One-Variable Function: Theory And Problems

The publication is devoted to theoretical and practical aspects of the subject of ‘Differentiation of One-Variable Function’, which is studied in the first and partially second terms in the first-year-course of mathematical analysis. It is based on the authors’ experience of reading lectures and conducting practical classes at the faculty of computational mathematics and cybernetics, Moscow State University.

The manual contains three chapters, the first of which is devoted to general theoretical aspects. This chapter contains basic concepts and facts related to the differentiation of functions, as well as some examples of the use of derivatives for solving various problems. The second chapter outlines the general scheme for investigating the function and constructing its graph, and gives recommendations on how to solve problems on finding the maximum (minimum) value of a function on a given set. It also shows some examples of the study of functions and the construction of their graphs, as well as an example of solving an applied problem for finding the maximum value of a function. The third chapter contains tasks (with solutions) for all the sections under consideration. Some of them are analyzed in the manual text while the others are designed to be solved on one’s own. For the second group of tasks, the answers and solutions are given at the end of the book in the corresponding section. The purpose of this manual is to help the student to learn the theoretical part and acquire practical skills in solving problems on the subject of ‘Differentiating a one-variable function’.

For university students. The publication can be useful for teachers who give lectures and conduct practical classes in mathematical analysis and all those who wish to study these subjects on their own or learn more about them.