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Basic Analysis: Introduction to Real Analysis

(2 reviews)

Jirí Lebl, Oklahoma State University

Pub Date: 2016

Publisher: Independent

Language: English

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Reviewed by Sonmez Sahutoglu, Associate Professor, University of Toledo on 8/22/16

This text covers all the standard material for a senior level undergraduate (or master level) real analysis class. It start with basics set theory and the real numbers. Then it develops supremum and infimum of bounded sets; limit, limsup, liminf... read more


Reviewed by William Newton, Research Scientist, Colorado State University on 1/8/16

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 introductory analysis class and skip the last two chapters for a slower class. read more


Table of Contents

  • Introduction
  • Chapter 1. Real Numbers
  • Chapter 2. Sequences and Series
  • Chapter 3. Continuous Functions
  • Chapter4. The Derivative
  • Chapter5. The Riemann Integral
  • Cjhapter6. 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.