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Elements of real analysis /

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Bibliographic Details
Main Author: Al-Gwaiz, M. A., 1942-
Corporate Author: Taylor & Francis
Other Authors: Elsanousi, S. A.
Format: eBook
Language:English
Published: Boca Raton, Fla. ; London : Chapman & Hall/CRC, ©2007.
Series:Monographs and textbooks in pure and applied mathematics ; 284.
Subjects:
Mathematical analysis.
Analyse mathématique.
Mathematical analysis
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Preface
  • 1. Preliminaries
  • 1.1. Sets
  • 1.2. Functions
  • 2. Real numbers
  • 2.1. Field axioms
  • 2.2. Order axioms
  • 2.3. Natural numbers, integers, rational numbers
  • 2.4. Completeness axiom
  • 2.5. Decimal representation of real numbers
  • 2.6. Countable sets
  • 3. Sequences
  • 3.1. Sequences and convergence
  • 3.2. Properties of convergent sequences
  • 3.3. Monotonic sequences
  • 3.4. The Cauchy criterion-- 3.5. Subsequences
  • 3.6. Upper and lower limits
  • 3.7. Open and closed sets
  • 4. Infinite series
  • 4.1. Basic properties
  • 4.2. Convergence tests
  • 5. Limit of a function
  • 5.1. Limit of a function
  • 5.2. Basic theorems
  • 5.3. Some extensions of the limit
  • 5.4. Monotonic functions
  • 6. Continuity
  • 6.1. Continuous functions
  • 6.2. Combinations of continuous functions
  • 6.3. Continuity on an interval-- 6.4. Uniform continuity
  • 6.5. Compact sets and continuity.
  • 7. Differentiation
  • 7.1. The derivative
  • 7.2. The mean value theorem
  • 7.3. L'Hôpital's rule
  • 7.4. Taylor's theorem
  • 8. The Riemann integral
  • 8.1. Riemann integrability
  • 8.2. Darboux's theorem and Riemann sums
  • 8.3. Properties of the integral
  • 8.4. The fundamental theorem of calculus
  • 8.5. Improper integrals
  • 8.5.1. Unbounded integrand
  • 8.5.2. Unbounded interval
  • 9. Sequences and series of functions
  • 9.1. Sequences of functions
  • 9.2. Properties of uniform convergence
  • 9.3. Series of functions
  • 9.4. Power series
  • 10. Lebesgue measure
  • 10.1. Classes of subsets of R
  • 10.2. Lebesgue outer measure
  • 10.3. Lebesgue measure
  • 10.4. Measurable functions
  • 11. Lebesgue integration
  • 11.1. Definition of the Lebesgue integral
  • 11.2. Properties of the Lebesgue integral
  • 11.3. Lebesgue integral and pointwise convergence
  • 11.4 Lebesgue and Riemann integrals
  • References
  • Notation
  • Index.