Elementary Real Analysis

Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner

Digital versions PDF
Source available No
Exercises Yes
Answers to selected exercises Yes, accompanied by hints
License Copyright retained by authors for all commercial uses
  • Text for two semesters of undergraduate real analysis
  • Two PDF versions
    • Hyperlinked and formatted for computer screens
    • Formatted for printing
  • May be printed for individual use but authors have reserved all rights for print distribution.
  • Published versions available as one or two volumes
    • Combined (740 pages, $33.95)
    • Volume I (400 pages, $17.95) and Volume II (290 pages, $16.95)
  • No solution manual
  • For more information and to download

This text was originally published by Prentice Hall in 2001. The second (and current) edition published in 2008 is essentially the same with misprints and other errors corrected. For a discussion of this text and the graduate analysis text by the same authors see the review by James Caragal in the UMAP Journal.

From the preface:

We have written this book in a leisurely style. This allows us to provide motivational discussions and historical perspective in a number of places. Even though the book is relatively large (in terms of number of pages), we can comfortably cover most of the main sections in a full-year course, including many of the interesting exercises.

Instructors teaching a short course have several options. They can base a course entirely on the unmarked material of Chapters 1, 2, 4, 5, and 7. As time permits, they can add the early parts of Chapters 3 and 8 or parts of Chapters 11 and 12 and some of the enrichment material.

Table of Contents

Volume I

  1. Properties of the Real Numbers
  2. Sequences
  3. Infinite Sums
  4. Sets of Real Numbers
  5. Continuous Functions
  6. More on Continuous Functions
  7. Differentiation
  8. The Integral
Volume II

  1. Sequences and Series of Functions
  2. Power Series
  3. The Euclidean Spaces Rn
  4. Differentiation on Rn
  5. Metric Spaces