Here, We provided Elements of Real Analysis By Shanti Narayan & M D Raisinghania is specially prepared for B.A., B.Sc., and honors (Mathematics and Physics), M.A/M.Sc. (Mathematics and Physics), B.E. Students of varied Universities and for I.A.S., P.C.S., AMIE, GATE, and other competitive exams. Almost all the chapters are rewritten in order that within the present form, the reader will not find any difficulty in understanding the topic matter. The matter of the previous edition has been re-organized in order that now each topic gets its proper place within the book. More solved examples are added in order that now each topic gets its proper place within the book. References to the newest papers of varied universities and that I .A.S. examination have been made at proper places.

Focusing on one among the most pillars of mathematics, Elements of Real Analysis By Shanti Narayan & M D Raisinghania provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the essential notions of limits and continuity during a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces.

Largely self-contained, the book begins with the elemental axioms of the important numeration system and gradually develops the core of the real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the idea of calculus on the important line, exploring limits, convergence tests, several functions like monotonic and continuous, series, and theorems like mean value, Taylor’s, and Darboux’s. The final chapters specialize in more advanced theory, especially, the Lebesgue theory of measure and integration.

**BOOK INFO**

**BOOK NAME** – ELEMENTS OF REAL ANALYSIS BY SHANTI NARAYAN & M D RAISINGHANIA

**AUTHOR** – SHANTI NARAYAN & M D RAISINGHANIA

**SIZE** – 13.0MB

**PAGES** – 744

Requiring only basic knowledge of elementary calculus, this textbook presents the required material for a primary course in real analysis. Developed by experts who teach such courses, it’s ideal for undergraduate students in mathematics and related disciplines, like engineering, statistics, computing, and physics, to know the foundations of real analysis.

Elementary Real Analysis may be a core course in nearly all mathematics departments throughout the planet. It avoids the compact sort of professional mathematics writing, in favor of a method that feels easier to students encountering the topic for the primary time. It presents topics in ways in which are most easily understood, yet doesn’t sacrifice rigor or coverage. In using this book, students discover that real analysis is totally deducible from the axioms of the important numeration system.

They learn the powerful techniques of limits of sequences because of the primary entry to the concepts of study and see the present role sequences play in virtually all later topics. They become comfortable with topological ideas and see how these concepts help unify the topic. Students encounter many interesting examples, including “pathological” ones, that motivate the topic and help fix the concepts.

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