Analysis has an important and central role in mathematics, so a course in analysis is usually required for students in several branches of the sciences, including mathematics, statistics, and economics. The present book is concise but introduces in detail important and fundamental concepts of analysis on the real line. This book covers the standard topics in undergraduate analysis and prepares the reader to study analysis on abstract spaces.
The book starts with fundamental concepts such as sets, real numbers and functions. The second chapter is about numerical sequences and the third one studies numerical series. The next chapter is about limits and continuity, and the following ones study theories of differentiation and integration of the functions. The last chapter studies the sequences and series of functions.
A remarkable part of the book consists of several good exercises, which are very suitable for students to work on. A number of exercises are indeed theorems and main facts, many of them are facts to prove, and only a few of them are computational. Short hints for selected exercises are given at the end of the book.
Since the book studies the concepts only on the real line, to read it a background in one variable calculus seems to be enough. The style is educational, brief, and not boring for beginners. Hence, the book is suitable for a first course in analysis.
Mehdi Hassani is a faculty member at the Department of Mathematics, Zanjan University, Iran. His field of interest is Elementary, Analytic and Probabilistic Number Theory.