This is a Mathematical analysis I textbook. This new course Mathematical analysis I, starting from the academic year 2004/2005, is taught at Faculty of Electronic Engineering Nis in the second semester. The book appeared after publishing the textbooks of the same authors, several times before, under the title “Mathematics for technical faculty students, part I” and “Mathematics for technical faculty students, part II”.
The textbook Mathematical analysis I comprises of 6 chapters. The last chapter is not (the Theory of Series) included by the syllabi of the previously mentioned course. This field is taught within mathematical courses at the second year of studies, at the Faculty of Electronic Engineering, Nis.
In Chapter “Real functions and their basic characteristics” is presented the very notion of a function, especially the notion of a real variable function, and then the basic properties of the real variable functions, such as: periodicity, monotonicity, convexity, notion of an inverse function, as well as notions of functions given parametrically and implicitly, but also notions of elementary and non-elementary functions. In the second part of this chapter is given a concept of metric and metric spaces, as well as basic topological notion.
Chapter Sequences consists of a part where notion of sequences and notion of its limit value are defined. Also, basic characteristics of convergent sequences and some limit values of sequences in the set of real numbers are explained. The chapter also comprises a part where notion of Cauchy’s sequences and notion of complete metric spaces is given.
Functions of a real variable is a chapter where the following notions are explained: notion of boundary values of real functions, characteristics of limit values, notion of continuity of functions as well as basic properties of continuous functions. Also this chapter explains some properties of monotonic functions, possibility of comparison of functions among themselves, symbols o and O, as well as uniform continuity of real functions.
In chapter Differentiation of functions of a real variable are presented: notions of derivative and differential of functions of first and higher order, basic theorems of differential calculus as well as their application in examination of basic characteristics of real functions. Also, this chapter defines singular points of curves, as well as notions of asymptotes of curves and curvatures of curves, and the notion of curve osculation. At the end of this chapter the graphic presentation of functions is studied.
Chapter Integration of functions of a real variable contains: indefinite integral, methods of integration of elementary functions, as well as notion of definite integrals, its characteristics and application of definite integral.
And in the end, in chapter Theory of series are presented numerical and functional series, types of convergence, as well as criteria for convergence of numerical and power series. Especially, trigonometric and Fourier series and their application are presented.
Every chapter is divided into sections, sections are divided into paragraphs.
All theoretical interpretations are backed up by adequate examples. At the end of each chapter is a section Exercises, with the aim to enable the users of this book to independently practice the previously exposed theories.
As the book is written in accordance with the newest syllabi and curriculum of studies at the Faculty of Electronic Engineering in Nis, it is above all, dedicated to students of Computer Science and Informatics, Telecommunications, Electronics and Electrical Engineering, but also to students of other technical faculties, as well as to students of Mathematics, Physics at Faculty of Science and Mathematics.