Understanding analysis /

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A textbook for an elementary, one-semester course in a mathematically rigorous approach to the study of functions of a real variable. Focuses on the questions that make the subject most interesting to new students, such as whether derivatives are integrable or continuous. Makes topics accessible by...

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Bibliographic Details
Call Number:QA300 A2.36
Main Author: Abbott, Stephen, 1964- (autor)
Format: Book
Language:Inglés
Published: New York : Springer, 2001.
Series:Undergraduate texts in mathematics
Subjects:
Mathematical analysis
Análisis matemático
Table of Contents:
  • 1. The Real Numbers.
  • 1.1. Discussion: The Irrationality of [square root of]2.
  • 1.2. Some Preliminaries.
  • 1.3. The Axiom of Completeness.
  • 1.4. Consequences of Completeness.
  • 1.5. Cantor's Theorem.
  • 2. Sequences and Series.
  • 2.1. Discussion: Rearrangements of Infinite Series.
  • 2.2. The Limit of a Sequence.
  • 2.3. The Algebraic and Order Limit Theorems.
  • 2.4. The Monotone Convergence Theorem and a First Look at Infinite Series.
  • 2.5. Subsequences and the Bolzano-Weierstrass Theorem.
  • 2.6. The Cauchy Criterion.
  • 2.7. Properties of Infinite Series.
  • 2.8. Double Summations and Products of Infinite Series.
  • 3. Basic Topology of R.
  • 3.1. Discussion: The Cantor Set.
  • 3.2. Open and Closed Sets.
  • 3.3. Compact Sets.
  • 3.4. Perfect Sets and Connected Sets.
  • 3.5. Baire's Theorem.
  • 4. Functional Limits and Continuity.
  • 4.1. Discussion: Examples of Dirichlet and Thomae.
  • 4.2. Functional Limits.
  • 4.3. Combinations of Continuous Functions.
  • 4.4. Continuous Functions on Compact Sets.
  • 4.5. The Intermediate Value Theorem.
  • 4.6. Sets of Discontinuity.
  • 5. The Derivative.
  • 5.1. Discussion: Are Derivatives Continuous?.
  • 5.2. Derivatives and the Intermediate Value Property.
  • 5.3. The Mean Value Theorem.
  • 5.4. A Continuous Nowhere-Differentiable Function.

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