**Best Reference Books on Real Analysis**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Real Analysis Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Real Analysis below.

1."Introduction to Real Analysis" by Robert G Bartle and Donald R Sherbert
“Introduction to Real Analysis” Book Review: This book serves as an introductory guide to real analysis, covering essential topics such as real numbers, sequences, and series, including limits and continuous functions. It also delves into differentiation, sequences of functions, infinite series, and offers a brief introduction to topology. The Riemann integral and the generalized Riemann integral are explored as well. Appendix A provides a comprehensive discussion on logic, proof of theorems, and various methods. The book incorporates helpful methods and tables with ample information. It is particularly valuable for graduate-level engineering and applied mathematics students.
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2."Elements of Real Analysis" by Narayan Shanti and Raisinghania M D
“Elements of Real Analysis” Book Review: This book provides a comprehensive introduction to the principles of real analysis. It covers essential topics such as sets and functions, the real number system, neighborhoods and limit points, and countability of sets. The book also explores real function limits and continuity, real-valued functions, and infinite series with positive and negative terms. With 22 chapters, it offers a thorough exploration of the subject matter. Additionally, the book includes recent question papers from examinations, making it a valuable resource for engineering students preparing for competitive exams like GATE and CSIR-UGC(NET).
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3."Real Analysis" by Royden
“Real Analysis” Book Review: This book serves as a comprehensive guide to the fundamental concepts of real analysis in mathematics. It covers various chapters including the classical theory of functions of a real variable, measure and integration theory, general topology, and normed linear space theory. Topics such as Lebesgue measure, Lebesgue measurable functions, differentiation, and integration are thoroughly explained. The book offers plenty of examples to facilitate students’ understanding of the topics and includes a vast number of practice problems for further reinforcement. It also provides insights into general topology and the theory of general Banach spaces, with a detailed explanation of normed linear space theory. Suitable for advanced mathematics and graduate-level engineering students, this book combines theory and examples to foster a solid understanding of the subject matter.
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4."Real Analysis" by Sharma and Vasishtha
“Real Analysis” Book Review: This book provides a comprehensive exploration of the core principles of real analysis in mathematics. It covers major chapters including the real and complex number systems, fundamental notions of set theory, elements of point set topology, and concepts of limits and continuity. Additionally, it delves into topics such as derivatives, Fourier series and Fourier integrals, multivariable differential calculus, implicit functions, and extremum problems. Each chapter is accompanied by exercises that allow students to practice and reinforce their understanding. This book serves as a valuable resource for students preparing for competitive exams such as IAS and PCS, offering them a solid foundation in real analysis.
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5."Real Analysis" by Karunakaran
“Real Analysis” Book Review: This book covers the main topics encompassing real analysis in a comprehensive manner. It explores the basic properties of the real number system, delves into finer aspects of set theory, investigates sequences and series, and examines the topological aspects of the real line. The book also discusses differentiation, functions of bounded variations, Riemann integration, and sequences and series of functions. At the end of each chapter, a collection of solved and unsolved exercises is provided to aid students in deepening their understanding and to serve as practice for testing purposes. With its focus on applied mathematics and its relevance to graduate-level engineering studies, this book is a valuable resource for students seeking a thorough understanding of real analysis.
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6."Real Analysis" by Carothers
“Real Analysis” Book Review: This book provides an overview of the basic concepts of real analysis in mathematics. It covers topics such as metric spaces, function spaces, the space of continuous functions, and functions of bounded variation. Other chapters include Lebesgue measure and integration, measurable functions, differentiation, and Fourier series. Each chapter concludes with a symbol index and references for further reading. This book is suitable for advanced mathematics and graduate-level engineering students.
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7."Basic Real Analysis" by Houshang H Sohrab
“Basic Real Analysis” Book Review: This book provides a comprehensive explanation of the fundamental principles of real analysis in calculus. It covers major chapters on set theory, sequences and series of real numbers, limits of functions, and the topology of R and continuity. Other topics discussed include metric spaces, the derivative, the Riemann integral, and sequences and series of functions. Each chapter concludes with a set of problems to test the students’ understanding. This book is a valuable resource for mathematics and engineering students.
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