A Textbook of B.Sc. Mathematics (Real Analysis), Semester II (Telangana State)

Product Overview & Details

The book has been carefully developed as per New Common Core Syllabus 2025-26 based on CBCS for B. Sc. First Year: Second Semester Students of the Universities in Telangana State. It offers a clear, rigorous, and student-friendly introduction to the foundational concepts of Real Analysis, forming a strong base for advanced mathematical studies.

    The text begins with the structure and properties of real numbers, including field axioms, order axioms, completeness and the supremum property. It then systematically develops the theory of Sequences, Sub sequences, Monotonic and Cauchy Sequences, followed by a detailed treatment of Infinite Series and Tests of convergence. The chapters on functions of a single variable present Limits, Continuity, Differentiability and Mean Value Theorems with logical proofs and illustrative examples. The book concludes with a comprehensive exposition of the Riemann Integral, covering integrability conditions, properties of integrals and the Fundamental Theorem of Calculus.

   Special emphasis is placed on conceptual clarity, step-by-step proofs, and problem-solving techniques. All chapters are supported with well-graded exercises and detailed solutions, making the book a dependable resource for examination preparation and self-study. 

• Fully aligned with Telangana State Universities Common Core Curriculum (CBCS), 2025-26
• Systematic coverage of Real Numbers, Sequences, Series, Continuity, Differentiation and Riemann Integration
• Clear exposition of completeness axiom, supremum-infimum concepts and Dedekind cuts
• Rigorous yet accessible presentation of theorems with proofs
• Logical progression from basic concepts to advanced analytical results
• Extensive coverage of Mean Value Theorems and their applications
• Well-structured chapters with definitions, theorems, illustrations and remarks
• Large collection of solved and unsolved problems for effective practice
• Detailed solutions provided at the end, aiding independent learning 
• Suitable for classroom teaching, examination preparation and a reference guide for aspirants of competitive exams