Vastavik Vishleshan (Real Analysis Hindi) by Dr. H.K. Pathak | B.A./B.Sc. 5th Semester DSC, All Chhattisgarh Universities | NEP | CSIR NET, UGC NET, GATE Mathematics & IIT JAM

Vastavik Vishleshan (Real Analysis) by Dr. H.K. Pathak is a Hindi-medium textbook written strictly to the B.A./B.Sc. 5th Semester (3rd Year) Discipline Specific Course syllabus of all Chhattisgarh State Universities, under the New Education Policy. Written in clear, accessible Hindi so students who think in their mother tongue can master rigorous proofs without a language barrier, it covers all four prescribed units in sequence: contributions and biography of Indian mathematicians, real numbers as an ordered field with completeness, Archimedean and nested interval properties; convergence of sequences including the Bolzano-Weierstrass theorem and Cauchy's convergence criterion; infinite series and every standard convergence test (comparison, D'Alembert's ratio, Cauchy root, Raabe's, logarithmic, Cauchy integral, Leibnitz's alternating series test); and Riemann integration with Darboux theorems and the fundamental theorem of integral calculus. This is the same rigorous content tested in CSIR NET, UGC NET, GATE Mathematics (MA) and IIT JAM Mathematics, both of which accept Hindi-medium candidates, so Hindi-medium students preparing for these exams are not left behind. Every theorem is proved step by step with worked examples in Hindi. The author, Dr. H.K. Pathak, is Professor & Head of the School of Studies in Mathematics at Pt. Ravishankar Shukla University, Raipur, with over 3,300 citations on Google Scholar and the Vijnana Parishad of India Distinguished Service Award (2011). Published by Shree Shiksha Sahitya Prakashan, this 470-page paperback First Edition (2026) is recommended across Hindi-medium universities and colleges for both the semester exam and competitive exam preparation.