This free online textbook is a one semester course in basic analysis. ...
This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course would. It should be possible to use these notes for a beginning of a more advanced course, but further material should be added.
Access also available here: https://www.jirka.org/ra/
Table of Contents 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