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Single Variable Differential and Integral Calculus

Elimhan Mahmudov
Atlantis Press
Publication Date: 
Number of Pages: 
[Reviewed by
Mehdi Hassani
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As its title suggests, the book under review is a friendly account of single-variable differential and integral calculus, but with a little bit more detail than one may expect of a calculus book. The contents are the usual material treated in a course on elementary undergraduate analysis in one variable. Apart from some typos, the text of the book is fluent and easy for self-study.

The author starts his book with a chapter introducing number systems and set theory, including metric spaces. Then, he studies sequences and series. After introducing limit and continuity of functions, he gives the concepts of differential and integral calculus and related topics. Several chapters of applications of these concepts end the book.

The sixth chapter of the book is about polynomials and interpolation, so is strongly related to numerical analysis. In this chapter, the author discusses factorization and finding the roots of polynomials.

The author starts on each topic in an easy way, much like a calculus book, but soon he enters topics from analysis. He gives many solved computational examples. Despite the fact that the text covers topics from elementary analysis, readers will find few problems on these topics. Instead, at the end of each chapter, there are lots of exercises, with final answers. Many of them have a computational flavor; indeed, they are exercises in elementary calculus or advanced calculus. The book contains a number of figures, but they are not satisfactorily clear, at least in the print version.

I believe that this book can be very used in parallel to a course in one variable calculus, or in one variable analysis. Instructors and students will find inside some very good examples of the topics they follow in class.

Mehdi Hassani is a faculty member at the Department of Mathematics, Zanjan University, Iran. His fields of interest are Elementary, Analytic and Probabilistic Number Theory.