000			02964nam a22001937a 4500
005			20240731101216.0
008			240731b |||||||| |||| 00| 0 eng d
020			_a9789354244612
082			_a515.8 _b BAR
100			_aBartle, Robert G
245			_aIntroduction to real analysis An Indian adaptation _cRobert G Bartle, Donald R Sherbert
250			_a4
260			_aNew Delhi _b Wiley _c2023
300			_a361P
505			_tCHAPTER 1 PRELIMINARIES 1.1 Sets and Functions 1.2 Mathematical Induction 1.3 Finite and Infinite Sets CHAPTER 2 THE REAL NUMBERS 2.1 The Algebraic and Order Properties of R 2.2 Absolute Value and the Real Line 2.3 The Completeness Property of R 2.4 Applications of the Supremum Property 2.5 Intervals CHAPTER 3 REAL SEQUENCES 3.1 Sequences and Their Limits 3.2 Limit Theorems 3.3 Monotone Sequences 3.4 Subsequences and the Bolzano-Weierstrass Theorem 3.5 The Cauchy Criterion 3.6 Properly Divergent Sequences CHAPTER 4 INFINITE SERIES 4.1 Introduction to Infinite Series 4.2 Absolute Convergence 4.3 Tests for Absolute Convergence 4.4 Tests for Nonabsolute Convergence CHAPTER 5 LIMITS 5.1 Limits of Functions 5.2 Limit Theorems 5.3 Some Extensions of the Limit Concept CHAPTER 6 CONTINUOUS FUNCTIONS 6.1 Continuous Functions 6.2 Combinations of Continuous Functions 6.3 Continuous Functions on Intervals 6.4 Uniform Continuity 6.5 Continuity and Gauges 6.6 Monotone and Inverse Functions CHAPTER 7 DIFFERENTIATION 7.1 The Derivative 7.2 The Mean Value Theorem 7.3 L’Hospital’s Rules 7.4 Taylor’s Theorem CHAPTER 8 THE RIEMANN INTEGRAL 8.1 Riemann Integral 8.2 Riemann Integrable Functions 8.3 The Fundamental Theorem 8.4 The Darboux Integral CHAPTER 9 SEQUENCES AND SERIES OF FUNCTIONS 9.1 Pointwise and Uniform Convergence 9.2 Interchange of Limits 9.3 Series of Functions 9.4 The Exponential and Logarithmic Functions 9.5 The Trigonometric Functions CHAPTER 10 THE GENERALIZED RIEMANN INTEGRAL 10.1 Definition and Main Properties 10.2 Improper and Lebesgue Integrals 10.3 Infinite Intervals 10.4 Convergence Theorems CHAPTER 11 A GLIMPSE INTO TOPOLOGY 11.1 Open and Closed Sets in R 11.2 Compact Sets 11.3 Continuous Functions 11.4 Metric Spaces CHAPTER 12 FUNCTIONS OF SEVERAL REAL VARIABLES
520			_aIntroduction to Real Analysis is a comprehensive textbook, suitable for undergraduate level students of pure and applied mathematics. Starting with the background of the notations for sets and functions and mathematical induction, the book focuses on real numbers and their properties, real sequences along with associated limit concepts, and infinite series. The book then explores the concepts of fundamental properties of limits and continuous functions, basic theory of derivatives and applications, including mean value theorem, chain rule, and inversion theorem.
650			_a Mathematical analysis Functions of real variables
942			_2ddc _cBK
999			_c2353 _d2353