Real Analysis

This book is designed to serve as a comprehensive textbook for undergraduate students studying at Indian universities and engineering institutes, including the prestigious Indian Institutes of Technology. Real Analysis is recognized as a core subject in undergraduate mathematics programs, and a solid grasp of this topic is essential for further study in advanced mathematics and related fields. The course typically requires a background in Higher Secondary level mathematics, particularly in calculus. However, to ensure accessibility for all students, the authors have thoughtfully included an introductory chapter on Set Theory. This addition makes the book more self-contained and suitable even for those who may need a refresher on foundational concepts. The text not only covers the fundamental topics expected in a first course in Real Analysis-such as sequences, series, limits, continuity, and differentiability-but also places strong emphasis on conceptual clarity. To support this goal, the authors have included a wide range of carefully selected examples throughout the book. These examples are aimed at enhancing student understanding and reinforcing key ideas by illustrating how theoretical concepts apply in practical contexts. Overall, this book stands as a valuable resource for undergraduate students of mathematics, offering both depth and clarity. It is especially helpful for those preparing for further studies or competitive examinations in mathematical sciences.