Elements of Real Analysis, 18e

Product Overview & Details

Elements of Real Analysis is a classic and convincing text that offers a rigorous, student-friendly introduction to the foundations of Real Analysis. Beginning from the basic concepts of sets, functions and the real number system, the book develops the subject systematically through sequences, series, limits, continuity, differentiation, Riemann and Riemann-Stieltjes integration, improper integrals, uniform convergence, power series, Fourier series and advanced topics such as functions of bounded variation.

In this edition, the book incorporates improved explanations, new theorems, additional solved examples and updated problems drawn from recent examinations. The authors present concepts with clarity and logical precision, making the text ideal for undergraduate and postgraduate students, as well as aspirants of competitive examinations like GATE, CSIR-UGC NET and IAS.

• Covers the entire syllabus for B.A./B.Sc., B.Sc. (Hons.), M.A./M.Sc., and engineering mathematics courses.

• More than 2,000 solved examples with step-by-step explanations for conceptual clarity.

• Extensive chapter coverage, including:

  Topology of the real line, countability, sequences and series

  Limits, continuity, differentiability and mean value theorems

  Riemann and Riemann-Stieltjes integrals

  Improper integrals, uniform convergence and power series

  Differentiation under the integral sign and Beta-Gamma functions

  Chapter on Functions of Bounded Variation

• Latest solved question papers from major universities, GATE (2005-2025), CSIR-UGC NET (2011-2025) and IAS examinations.

• Modern notation, intuitive explanations, and logical development make the subject accessible without compromising rigour.

• Rich pedagogical aids including illustrations, remarks, counterexamples, and self-practice exercises.

• Glossary of Symbols, Index and lists of important results for quick reference.

Clear, comprehensive, and reliable, the book remains an indispensable resource for mastering the principles of Real Analysis and building a strong mathematical foundation for advanced study and research.