AIM Open Textbook Initiative

The following book has met the evaluation criteria developed by the AIM Editorial Board.

Basic Analysis: Introduction to Real Analysis
  Jiri Lebl

Digital versions	pdf
Source available	Yes
Exercises	Yes
Answers	No
Solution manual	No
License	Creative Commons Attribution-NonCommercial-ShareAlike

• 192 page text for one semester of undergraduate real analysis
• Contains 199 exercises
• Class tested
• Printed copy available from Lulu for $13.42
• List of course adoptions available
• For more information and to download

The book is quite new but has already been used by a number of other faculty at other institutions who say that they recommend the book and would use it again. This book originated as lecture notes for the undergraduate analysis course at the University of Illinois in 2009, and so it follows the syllabus for that course based on the text of Bartle and Sherbert.

There are seven chapters: Real Numbers, Sequences and Series, Continuous Functions, The Derivative, The Riemann Integral, Sequences of Functions, Metric Spaces. For a significant application of the concepts already developed, chapter 6 contains a rigorous treatment of Picard's theorem on the existence and uniqueness of solutions of ordinary differential equations.

In order to promote the book's longevity the author notes:

"The book can be updated and modified even if I happen to drop off the face of the earth. You do not have to depend on any publisher being interested as with traditional textbooks. Furthermore, errata are fixed promptly, meaning simply that if you teach the same class next term, all errata that are spotted are already fixed. No need to wait several years for a new edition."