Dutta H., Natarajan P.N., Cho Y.J. Concise Introduction to Basic Real Analysis

CRC Press; Taylor & Francis Group, 2020. — 253 p. — ISBN: 9780429464676.This book provides an introduction to basic topics in Real Analysis and makes the subject easily understandable to all learners. The book is useful for those that are involved with Real Analysis in disciplines such as mathematics, engineering, technology, and other physical sciences. It provides a good balance while dealing with the basic and essential topics that enable the reader to learn the more advanced topics easily. It includes many examples and end of chapter exercises including hints for solutions in several critical cases. The book is ideal for students, instructors, as well as those doing research in areas requiring a basic knowledge of Real Analysis. Those more advanced in the field will also find the book useful to refresh their knowledge of the topic.
Features
Includes basic and essential topics of real analysis Adopts a reasonable approach to make the subject easier to learn Contains many solved examples and exercise at the end of each chapter Presents a quick review of the fundamentals of set theory Covers the real number system Discusses the basic concepts of metric spaces and complete metric spacesReview of Set Theory
The Real Number System
Sequences and Series of Real Numbers
Completeness Axiom, Archimedean Property of R
Metric Spaces { Basic Concepts, Complete Metric Spaces
Limits and Continuity
Connectedness and Compactness
Differentiation
Integration
Sequences and Series of Functions