This textbook has been designed to meet the needs of B.Sc. Second Semester (Core III) students of Mathematics as per Common Minimum Syllabus prescribed for Odisha University and other Universities and Colleges under the recommended National Education Policy 2020 in Odisha. This book is a comprehensive guide designed for undergraduate mathematics students. This textbook precisely covers fundamental concepts and advanced topics in real analysis, making it an essential resource for academic success. Organized into Four Units, the book begins with Cardinality of Sets and explores the properties of Real Numbers, including Supremum, Infimum, and Dedekind's theory. It explores the sequences and series, addressing convergence criteria, the Bolzano-Weierstrass Theorem, and tests for Series Convergence. The study of Infinite Series, including Geometric, Logarithmic, and Binomial Series, is presented with clarity, alongside Alternating Series and Leibniz Tests. The final unit focus on the Limit of Functions and Continuity, exploring L'Hôpital's Rule, indeterminate forms, and theorems such as Borel's and Bolzano's. Whether you're aiming to master the foundations of real analysis or preparing for advanced studies, this textbook serves as a trusted companion for Semester II.
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