INDICE: 1. Preliminaries. 1.1 Sets and Functions 1.2 Mathematical Induction1.3 Finite and Infinite Sets 2. The Real Numbers. 2.1 The Algebraic and OrderProperties 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 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 4. Limits. 4.1 Limits of Functions 4.2 Limit Theorems 4.3 Some Extensions of the Limit Concept 5. Continuous Functions. 5.1 Continuous Functions 5.2 Combinations of Continuous Functions 5.3 Continuous Functions on Intervals 5.4 Uniform Continuity 5.5 Continuity and Gauges 5.6 Monotone and Inverse Functions 6. Differentiation. 6.1 The Derivative 6.2 The Mean Value Theorem 6.3 LHospitals Rules6.4 Taylors Theorem 7. The Riemann Integral. 7.1 The Riemann Integral 7.2 Riemann Integrable Functions 7.3 The Fundamental Theorem 7.4 Approximate Integration 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 9. Infinite Series. 9.1 Absolute Convergence 9.2 Tests for Absolute Convergence 9.3 Tests for Nonabsolute Convergence 9.4 Series of Functions 10. The Generalized Riemann Integral. 10.1 Definition and Main Properties 10.2 Improper and Lebesgue Integrals 10.3 Infinite Intervals 10.4 Convergence Theorems 11. A Glimpse into Topology. 11.1 Open and Closed Sets in R 11.2 Compact Sets 11.3 Continuous Functions 11.4 Metric 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. References. Photo Credits. Hints for Selected Exercises. Index.
- ISBN: 978-0-471-43331-6
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 402
- Fecha Publicación: 04/01/2011
- Nº Volúmenes: 1
- Idioma: Inglés