Kindly note that we have put a lot of effort into researching the best books on Real Analysis subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Real Analysis" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.
1. “Principle of Mathematical Analysis” by Walter Rudin
“Principle of Mathematical Analysis” Book Review: This book explains the fundamentals of mathematical analysis. Major chapters included are real number systems, development of convergence, continuity, differentiation and integration. A brandnew section is added on the gamma function. Multiple exercises are added for students to get the best out of the book. This book is suitable for undergraduate or first year graduate students.


2. “Theory and Application of Infinite Series” by K Knopp
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“Theory and Application of Infinite Series” Book Review: This book covers the Core principles and applications of infinite series. The main chapters discussed are principles of the theory of real numbers, sequences of real numbers, series of positive terms, series of arbitrary terms. Other topics mentioned are power series, expansions of the socalled elementary functions, infinite products. Exercises at the end of every chapter to practice. All the topics and formulas are discussed in detail. Students studying undergraduate engineering can use this book.


3. “Mathematical Analysis” by T M Apostol
“Mathematical Analysis” Book Review: This book provides Advanced topics on real and complex function theory. Main chapters included are real and complex number systems, set theory, limits and continuity. Other topics mentioned are Derivatives, functions of bounded variation, infinite products, sequences of functions, Riemannstieltjes integral. All the topics and theorems are described in detail. Numerous problems and their respective solutions are provided for students’ practice. This book is useful for students studying graduate level engineering or advanced level mathematics.


4. “Foundations of Mathematical Analysis” by Richard Johnsonbaugh
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“Foundations of Mathematical Analysis” Book Review: This book discusses the foundation of mathematical Analysis. Main chapters covered are infinite series, limits of real valued functions, metric spaces, differential calculus of the real line. Other topics mentioned are sequences and series of functions, transcendental functions, inner product spaces and Fourier series. over 750 exercises are added in this book for students’ practice. It also includes 34 figures to explain methods and equations easily. This book is useful for graduate engineering or applied mathematics students.


5. “Introduction to Real Analysis” by Robert G Bartle and Donald R Sherbert
“Introduction to Real Analysis” Book Review: This book is an introduction to real analysis. Main chapters discussed are the real numbers, sequences and series cover limits, continuous functions. Other topics included are differentiation, sequences of functions, infinite series, a glimpse into topology. The Riemann integral and the generalized Riemann integral are also discussed. Logic and proofs of theorems and methods are provided in appendix a. All the methods and tables are displayed with sufficient information. This book is useful for graduate level engineering and applied mathematics students.


6. “Elements of Real Analysis” by Narayan Shanti and Raisinghania M D
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“Elements of Real Analysis” Book Review: This book presents the elements of real analysis. The main topics included are set and functions, the real number, neighbours and limit points of a set and countability of sets. Other topics discussed are real function limits and continuity, real functions, infinite series with positive and negative terms. This book consists of 22 chapters along with latest question papers asked in the examination. Students studying for engineering examinations and preparing for competitive exams such as GATE, CSIRUGC(NET) Can refer to this book.


7. “Real Analysis” by Royden
“Real Analysis” Book Review: This book explains the fundamental concepts of real analysis in mathematics. chapters discussed are the classical theory of functions of a real variable, measure and integration theory, general topology and normed linear space theory. Other topics included are Lebesgue measure, Lebesgue measurable functions, Differentiation and integration. plenty of examples are provided for students to understand the topic easily. Huge number of problems are provided for students’ practice. This book is suitable for advanced mathematics and graduate level engineering students.


8. “Real Analysis” by Sharma and Vasishtha
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“Real Analysis” Book Review: This book describes the core principles of real analysis in mathematics. Major chapters included are the real and complex number systems, some basic notions of set theory, elements of point set topology, limits and continuity. Other topics included are derivatives, fourier series and fourier integrals, multivariable differential calculus, implicit functions and extremum problems. Exercises at the end of every chapter are provided for students to practice. Students studying for competitive exams such as IAS, PCS can refer to this book.


9. “Real Analysis” by Karunakaran
“Real Analysis” Book Review: This book consists of the main topics regarding real analysis. The main topics included are basic properties of the real number system, some finer aspects of set theory, sequences and series, topological aspects of the real line. Other topics mentioned are differentiation, functions of bounded variations, Riemann integration, Sequences and series of functions. Solved exercises and unsolved exercises are added at the end of every chapter for students to better understand and test purposes. Applied mathematics or graduate level engineering students can use this book.


10. “Real Analysis” by Carothers
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“Real Analysis” Book Review: This book covers the basic concepts of real analysis in mathematics. The main topics mentioned are metric spaces, function spaces, the space of continuous functions, functions of bounded variation. Other chapters included are Lebesgue measure and integration, Measurable functions, differentiation, fourier series. Definition, notes and remarks are added at the end of every chapter. At the end of the book symbol index and references are added for quick review and further reading purposes. This book is suitable for advanced mathematics and graduate level engineering students.


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