Basic Analysis I: Introduction to Real Analysis, Volume I

Version 5.6. (Newer edition 6 available ISBN: 979-8851944635) A first course in rigorous mathematical analysis. Covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, sequences of functions, and metric spaces. Originally developed to teach Math 444 at University of Illinois at Urbana-Champaign and later enhanced for Math 521 at University of Wisconsin-Madison and Math 4143 at Oklahoma State University. The first volume is either a stand-alone one-semester course or the first semester of a year-long course together with the second volume. It can be used anywhere from a semester early introduction to analysis for undergraduates (especially chapters 1-5) to a year-long course for advanced undergraduates and masters-level students. See http://www.jirka.org/ra/

Table of Contents (of this volume I):
Introduction
1. Real Numbers
2. Sequences and Series
3. Continuous Functions
4. The Derivative
5. The Riemann Integral
6. Sequences of Functions
7. Metric Spaces

This first volume contains what used to be the entire book "Basic Analysis" before edition 5, that is chapters 1-7. Second volume contains chapters on multidimensional differential and integral calculus and further topics on approximation of functions.

Jiri Lebl is an Associate Professor in the Department of Mathematics at the Oklahoma State University. Jiri has taught mathematics at all levels for well over a decade at several other institutions: San Diego State University, University of California at San Diego, University of Illinois at Urbana-Champaign, and University of Wisconsin-Madison. He has published over 30 peer reviewed scientific papers, mostly focused on complex analysis in several variables. Before jumping fully into mathematics, he was involved in programming and free software, in particular, the GNOME desktop project, and he wrote several programming tutorials.