04136nam a22003734a 4500999001700000001000600017003000900023005001700032008004100049010001700090020001800107020002900125020002600154035002400180040006000204042000800264050002200272082001200294100004200306245007500348250001900423260004900442300004700491504005100538505206000589520078002649526000803429650003403437650004003471700003903511852004003550942001203590952016003602  c40728d4072834638BD-DhAAL20190509095035.0190509r20152018njua     b    001 0 eng d  a  2010045251  a9788126551811  a9780471433316 (hardback)  a0471433314 (hardback)  a(OCoLC)ocn671573454  aDLCcDLCdYDXdYDXCPdBWXdCUSdCDXdIULdDLCdBD-DhAAL  apcc00aQA300b.B294 201100a5152221 aBartle, Robert Gardner,d1927-93155710aIntroduction to real analysis /cRobert G. Bartle, Donald R. Sherbert.  aFourth edition  aHoboken, NJ :bWiley,c2015 [reprinted 2018]  axiii, 402 pages :billustrations ;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"--  aMNS 0aMathematical analysis.931558 0aFunctions of real variables.9315591 aSherbert, Donald R.,d1935-931560  aAyesha Abed LibrarycGeneral Stacks  2ddccBK  00102ddc4070aBRACULbBRACULcGENd2019-04-24eMullick & Brothersg670.00l6m45o515 BARp3010034638r2026-06-27s2026-05-07t1v670.00w2019-04-24yBK