1. “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.
2. “Elements of Real Analysis” by Narayan Shanti and Raisinghania M D
“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, CSIR-UGC(NET) Can refer to this book.
3. “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 gives information on general topology and the theory of general Banach spaces. A detailed explanation on normed linear space theory is given in this book. This book contains examples which helps in understanding of concepts. This book is suitable for advanced mathematics and graduate level engineering students.
4. “Real Analysis” by Sharma and Vasishtha
“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.
5. “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.