This free online textbook (OER more formally) is a course in undergraduate real analysis (somewhere it is called "advanced calculus"). The book is meant both for a basic course for students who do not necessarily wish to go to graduate school, but also as a more advanced course that also covers topics such as metric spaces and should prepare students for graduate study. A prerequisite for the course is a basic proof course. An advanced course could be two semesters long with some of the second-semester topics such as multivariable differential calculus, path integrals, and the multivariable integral using the second volume. There are more topics than can be covered in two semesters, and it can also be reading for beginning graduate students to refresh their analysis or fill in some of the holes.
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UMSL OER Adopted
CreateSpace Independent Publishing Platform; 5th edition
This OER at UMSL
Prof. David Covert - MATH 4100
Lebl, Jiří, "Basic Analysis: Introduction to Real Analysis" (2009). Open Educational Resources Collection. 30.
Available at: https://irl.umsl.edu/oer/30