A Textbook of B.Sc. Mathematics Real Analysis: For B.A/B.Sc. Mathematics 2nd Year | Andhra Pradesh University

This book is designed for B.A./B. Sc. Mathematics Second Year (Second Semester) Students of the Universities in Andhra Pradesh. Designed to strengthen your foundational understanding, this book effortlessly merges the theory with practical applications, making complex concepts accessible and engaging. The book is divided into Five Units. Unit I: Real Numbers and Real Sequences explore the algebraic and order properties of real numbers, the completeness property, and the intricacies of sequences, including convergence, monotonicity, and the Bolzano-Weierstrass theorem. Unit II: Infinite Series develop a thorough understanding of evaluating series using convergence tests such as the p-test, Root Test, Ratio Test, and the Leibniz Test for alternating series. Unit III: Limits and Continuity understand the limits of real-valued functions, the concept of continuity, and uniform continuity through rigorous yet simplified explanations. Unit IV: Differentiation and Mean Value Theorems grasp the essence of differentiation and delve into the profound implications of Rolle's, Lagrange's, and Cauchy's Mean Value Theorems. Unit V: Riemann Integration achieve a deep understanding of the Riemann integral, exploring the properties of integrable functions, the Fundamental Theorem of Calculus, and its practical applications as a limit of sums.