Basic Analysis: Introduction to Real Analysis

(2 reviews)


Jirí Lebl, Oklahoma State University

Pub Date: 2016

ISBN 13:

Publisher: Independent

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Reviewed by Sonmez Sahutoglu, Associate Professor, University of Toledo, on 8/22/2016.

This text covers all the standard material for a senior level undergraduate (or master level) real analysis class. It start with basics set theory … read more



Reviewed by William Newton, Research Scientist, Colorado State University, on 1/8/2016.

The textbook covers everything I would want to cover in a course at this level and some more. A teacher can use this book as the sole text of an … read more


Table of Contents

  • Introduction
  • Chapter 1. Real Numbers 
  • Chapter 2. Sequences and Series 
  • Chapter 3. Continuous Functions 
  • Chapter 4. The Derivative 
  • Chapter 5. The Riemann Integral 
  • Cjhapter 6. Sequences of Functions 
  • Chapter 7: Metric Spaces (New in November 18th 2011 edition)

About the Book

This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.

About the Contributors


Jirí Lebl, Assistant Professor, Department of Mathematics, Oklahoma State University.