Descript 
xiii, 402 pages : illustrations ; 26 cm 

text rdacontent 

unmediated rdamedia 

volume rdacarrier 
Note 
Includes bibliographical references and index 
Contents 
Ch. 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 BolzanoWeierstrass 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 
Note 
"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 userfriendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing pointset 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" Provided by publisher 
LC subject 
Mathematical analysis


Functions of real variables

Add Author 
Sherbert, Donald R., 1935

ISBN 
9780471433316 (hardback) 

0471433314 (hardback) 
