000			03993cam a22003254a 4500
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003			UG-KaMUL
005			20250613004020.0
010			_a2010-045251
020			_a9780471433316 (hardback)
020			_a0471433314 (hardback)
039			_a202203091402 _b 958 _c 202203091358 _d 958 _c 202203091354 _d 958 _c 202102101921 _d 958 _y 201509211446 _z959
040			_aDLC _c DLC _d YDX _d YDXCP _d BWX _d CUS _d CDX _d IUL _d DLC _d UG- KaMUL
082			_a515.8 _2 23
092			_a515.8 BAR
100			_aBartle, Robert Gardner, _d 1927-
245			_aIntroduction to real analysis / _cRobert G. Bartle, Donald R. Sherb ert.
250			_a4th ed.
260			_aHoboken, NJ : _bWiley, _c c2011.
300			_axiii, 402 p. : _bill. ; _c 26 cm.
504			_aIncludes bibliographical references and index.
505			_aCh. 1.Preliminaries: 1.1. Sets and functions; 1.2. Mathematical indu ction; 1.3. Finite and infinite sets -- Ch. 2. The Real Numbers: 2.1. T he algebraic and order properties of R; 2.2. Absolute value and real li ne; 2.3. The completeness property of R; 2.4. Applications of the supr emum property; 2.5. Intervals -- Ch. 3. Sequences and series: 3.1. Sequ ences and their limits; 3.2. Limit theorems; 3.3. Monotone sequences; 3 .4. Subsequences and the Bolzano-Weierstrass theorem; 3.5. The Cauchy c riterion; 3.6. Properly divergent sequences; 3.7. Introduction to infin ite series -- Ch. 4. Limits: 4.1. Limits of functions; 4.2. Limit theor ems; 4.3. Some extensions of the limit concept -- Ch. 5. Continuous fun ctions: 5.1. Continuous runctions; 5.2 . Combinations of continuous run ctions; 5.3. Continuous functions on intervals; 5.4. Uniform continuity ; 5.5. Continuity and gauges; 5.6. Monotone and inverse functions -- Ch . 6. Differentiation: 6.1. The derivative; 6.2. The mean value theorem ; 6.3. L'Hospital's rules; 6.4. Taylor's Theorem -- Ch. 7. The Riemann integral: 7.1. Riemann integral; 7.2. Riemann integrable functions; 7.3 . The fundamental theorem; 7.4. The Darboux integral; 7.5. Approximate integration -- Ch. 8. Sequences of functions: 8.1. Pointwise and unifor m convergence; 8.2. Interchange of limits; 8.3. The exponential and log arithmic functions; 8.4. The trigonometric functions -- Ch. 9. Infinite series: 9.1. Absolute convergence; 9.2. Tests for absolute convergence ; 9.3. Tests for nonabsolute convergence; 9.4. Series of functions -- C h. 10. The generalized Riemann integral: 10.1. Definition and main pope rties; 10.2. Improper and Lebesgue integrals; 10.3. Infinite intervals; 10.4. Convergence theorems -- Ch. 11. A glimpse into topology: 11.1. O pen and closed sets in R; 11.2 Compact sets; 11.3. Continuous functions ; 11.4. Metrtic Spaces -- Appendix A. Logic and proofs -- Appendix B. F inite and countable sets -- Appendix C. The Riemann and Lebesgue criter ia -- Appendix D. Approximate integration -- Appendix E. Two examples.
520			_a"This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the a bility to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition ma intains the same spirit and user-friendly approach with addition exampl es and expansion on Logical Operations and Set Theory. There is also co ntent revision in the following areas: introducing point-set topology b efore discussing continuity, including a more thorough discussion of li msup and limimf, covering series directly following sequences, adding c overage of Lebesgue Integral and the construction of the reals, and dra wing student attention to possible applications wherever possible"-- _c Provided by publisher.
650			_aMathematical analysis.
650			_aFunctions of real variables.
700			_aSherbert, Donald R., _d 1935-
942			_2ddc _cBK
999			_c558658 _d558658