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001			015773217
003			Uk
005			20170830172512.0
008			101022s2011 njua b 001 0 eng
010			_a2010045251
016	7		_a015773217 _2Uk
020			_a9788126551811
035			_a(OCoLC)ocn671573454
040			_aIISER Bhopal _cIISER Bhopal
042			_aukblcatcopy
050	0	0	_aQA300 _b.B294 2011
082	0	0	_a515 B284I4 _223
100	1		_aBartle, Robert G. _921767
222			_aMathematics-textbook Collection
245	1	0	_aIntroduction to real analysis _cRobert G. Bartle, Donald R. Sherbert.
250			_a4th ed.
260			_aNew Delhi : _bWiley India Pvt. Ltd., _c2017.
300			_axiii, 402 p. : _bill. ; _c26 cm.
504			_aIncludes bibliographical references and index.
505	0		_aCh. 1.Preliminaries: 1.1. Sets and functions; 1.2. Mathematical induction; 1.3. Finite and infinite sets -- Ch. 2. The Real Numbers: 2.1. The algebraic and order properties of R; 2.2. Absolute value and real line; 2.3. The completeness property of R; 2.4. Applications of the supremum property; 2.5. Intervals -- Ch. 3. Sequences and series: 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; 3.7. Introduction to infinite series -- Ch. 4. Limits: 4.1. Limits of functions; 4.2. Limit theorems; 4.3. Some extensions of the limit concept -- Ch. 5. Continuous functions: 5.1. Continuous runctions; 5.2 . Combinations of continuous runctions; 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 uniform convergence; 8.2. Interchange of limits; 8.3. The exponential and logarithmic 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 -- Ch. 10. The generalized Riemann integral: 10.1. Definition and main poperties; 10.2. Improper and Lebesgue integrals; 10.3. Infinite intervals; 10.4. Convergence theorems -- Ch. 11. A glimpse into topology: 11.1. Open and closed sets in R; 11.2 Compact sets; 11.3. Continuous functions; 11.4. Metrtic Spaces -- Appendix A. Logic and proofs -- Appendix B. Finite and countable sets -- Appendix C. The Riemann and Lebesgue criteria -- 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 ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible"--
650		0	_aMathematical analysis. _921768
650		0	_aFunctions of real variables. _921769
700	1		_aSherbert, Donald R., _921770
942			_2ddc _cBK
999			_c8213 _d8213