Real Analysis
by Dr. H.K. Pathak
₹370
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About this book
Real Analysis by Dr. H.K. Pathak is the syllabus-exact textbook for B.A./B.Sc. 5th Semester Discipline Specific Course students across all Chhattisgarh State Universities, built strictly to the NEP curriculum. All four prescribed units are covered in university sequence, opening with the contributions of Indian mathematicians — Swami Bharati Krishna Tirth, Madhav, Neelkanth Somayaji and Srinivasa Ramanujan Iyengar.
Real Analysis is also the core paper tested in CSIR NET, UGC NET, GATE Mathematics (MA) and IIT JAM Mathematics, so students preparing for those exams get the same rigorous foundation from one book. Each theorem is proved step by step with solved examples, so students can follow the logic rather than memorise results.
Dr. H.K. Pathak is Professor and Head of the School of Studies in Mathematics at Pt. Ravishankar Shukla University, Raipur, with over 3,300 Google Scholar citations and the Vijnana Parishad of India Distinguished Service Award (2011). Published by Shree Shiksha Sahitya Prakashan, Meerut.
Syllabus coverage
Unit 1 · Real Numbers
Contributions of Indian mathematicians; Real numbers as an ordered field; Least upper bound property; Completeness of R; Archimedean property; Dense subsets; Nested intervals; Neighbourhoods, limit points, open, closed and perfect sets
Unit 2 · Sequences
Bounded and monotonic sequences; Limit theorems; Monotone convergence theorem; Subsequences; Bolzano-Weierstrass theorem; Limit superior and inferior; Cauchy sequences and Cauchy's criterion
Unit 3 · Infinite Series
Convergence and divergence; Comparison test; D'Alembert's ratio test; Cauchy root test; Raabe's test; Logarithmic test; Cauchy integral test; Alternating series and Leibnitz's test; Absolute and conditional convergence; Rearrangement; Riemann's theorem
Unit 4 · Riemann Integration
Riemann integrability; Darboux theorems; Fundamental theorem of integral calculus; Improper integrals