04088cam a22003494a 4500999001500000001000900015003000400024005001700028008004100045010001700086020002900103020002600132035002400158040005100182042000800233050002200241082002500263100003500288245007500323250001200398260003400410300003500444504005100479505206000530520080402590650002703394650008203421700003203503906004503535942001303580952014503593  c3332d333216513689OSt20250225175319.0101022s2011    njua     b    001 0 eng    a  2010045251  a9780471433316 (hardback)  a0471433314 (hardback)  a(OCoLC)ocn671573454  aDLCcKyULdYDXdYDXCPdBWXdCUSdCDXdIULdDLC  apcc00aQA 300b.B37 201100aQA 300 .B37 20112221 aBartle, Robert Gardner,d1927-10aIntroduction to real analysis /cRobert G. Bartle, Donald R. Sherbert.  a4th ed.  aHoboken, NJ :bWiley,cc2011.  axiii, 402 p. :bill. ;c26 cm.  aIncludes bibliographical references and index.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.  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"--cProvided by publisher. 0aMathematical analysis. 0aFunctions of real variables.2StatisticsxSchool of Pure and Applied Sciences1 aSherbert, Donald R.,d1935-  a7bcbccorignewd1eecipf20gy-gencatlg  2lcccLLB  00102lcc40708NFICaKyUCLbKyUCLcGENd2017-02-09ePurchasel12oQA 300 .B37 2011pKYU/2017/5614r2026-03-31s2025-03-17w2017-02-09yLLB