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Real Analysis - I | Mathematics for B.Sc. Students | Semester II (Core III) | As per NEP 2020 Model Syllabus - NEP 2020 Odisha

Real Analysis - I | Mathematics for B.Sc. Students | Semester II (Core III) | As per NEP 2020 Model Syllabus - NEP 2020 Odisha

Author : H K Dass, Rajnish Verma & Rama Verma

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  • ISBN : 9789364689052
  • Pages : 296
  • Binding : Paperback
  • Language : English
  • Imprint : S Chand Publishing
  • © year : 2025
  • Size : 6.50*9.25

Price : 275.00 220.00

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.

  1. Very lucid and logical presentation of concepts, for easy and quick understanding.
  2. More than 200 examples for easy understanding of concepts
  3. More than 850 exercise questions strengthen the well-explained theoretical concepts.
  4. A section on Multiple Choice Questions (MCQs) to enhance understanding and exam readiness.

Unit I

1. Cardinality of a Set
2.  Algebraic and Order Properties of R
3. Applications of Supremum Property, Intervals, Nested Interval Property Denseness of Rationals in R

Unit II

4. Sequence and Convergence
5. Cauchy Sequence and Convergence

Unit III

6. Infinite Series and Convergence
7. Tests for Convergence
8. Alternating Series, Leibniz Test, Absolute and Conditional Convergence

Unit IV

9. Limit of Functions
10. Continuity

MULTIPLE CHOICE QUESTIONS (MCQs)

EXAMINATION PAPERS

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.

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