Understanding Analysis – Stephen Abbott – 1st Edition


Understanding Analysis outlines an elementary; one-semester course designed to expose students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable.

The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on the questions that give analysis its inherent fascination.

Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Are derivatives continuous? Are derivatives integrable? Is an infinitely differentiable function necessarily the limit of its Taylor series? In giving these topics center stage; the hard work of a rigorous study is justified by the fact that they are inaccessible without it.

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  • The Real Numbers
    Sequences and Series
    Basic Topology of R
    Functional Limits and Continuity
    The Derivative
    Sequences and Series of Functions
    The Riemann Integral
    Additional Topics
  • Citation
    • Full Title: Understanding Analysis
    • Author/s:
    • ISBN-13: 9780387215068
    • Edition: 1st Edition
    • Topic: Math
    • Subtopic: Numerical Analysis
    • File Type: eBook | Solution Manual
    • Idioma: English

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