Ludmila Bourchtein is Professor Emeritus and Senior Research Scientist at the Institute of Physics and Mathematics, Federal University of Pelotas, Brazil. She received her Ph.D. in Mathematics from Saint Petersburg State University, Russia. During the span of 34 years at the Mathematics Institute, Far East State University, Russia, she held different positions, from Assistant Professor, Associate Professor, to the rank of Full Professor. In the last 15 years, she served as Associate and Full Professor at the Institute of Physics and Mathematics, Federal University of Pelotas, where she was conferred with the title of Emeritus Professor in 2019. An author of more than 80 referred articles and 6 books, her research interests include real and complex analysis, conformal mappings and numerical analysis. During her research career, she was awarded a number of grants of Russian and Brazilian science foundations and scientific societies, including the International Mathematical Union (IMU) and the International Council for Industrial and Applied Mathematics (ICIAM).

Gives a gradual development of the material starting from the background topics related to real numbers and functions

Presents a strict mathematical approach to the study of elementary functions

Includes a large number of examples and exercises, both solved and proposed

- 1. Sets of Numbers and Cartesian Coordinates. - 2. Functions and Their Analytic Properties. - 3. Algebraic Functions: Polynomial, Rational and Irrational. - 4. Transcendental Functions: Exponential, Logarithmic, Trigonometric. - 5. Epilogue: A Bridge to Calculus.