Includes bibliographical references and index.

Ch. 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.

"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"-- Provided by publisher.