Basic Analysis I: Introduction to Real Analysis, Volume I

by Jiří Lebl

Version 6.0. 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 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.

Genres: Mathematics, Textbooks

312 pages, Paperback

First published December 16, 2014

Reviews

[Satyaki · Rating 5 out of 5]

https://www.youtube.com/playlist?list...

https://ocw.mit.edu/courses/18-100a-r...

[Asia | Adventures with Asia Minor · Rating 4 out of 5]

8 December 2023

4 stars!

*Technically finished up to Section 4.2 (Mean Value Theorem)*

Okay, for a textbook, this wasn't that bad. No real review since it is just a textbook for college. It's not the best real analysis textbook (or so I've been told by my professor), but for one that's available for free online, it's not that bad. . . .

Anyway, it wasn't bad. The end. XD

4 stars!

~~~~~

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Happy Reading!

[Matthew Zabka · Rating 5 out of 5]

I have chosen this textbook for the undergraduate real analysis course I am teaching, and I think it is wonderful. Some notes:

The text layout is simple, clear, and concise.
The exercises vary in difficulty from testing a student's understanding of a definition to testing a student's understanding of difficult proofs.
Until the later chapters, the author has chosen to do everything in R. This diminishes the impact of some important results (e.g. the Bolzano–Weierstrass theorem), but overall makes concepts much simpler for students to understand.

[Nicholas Cotton · Rating 4 out of 5]

It’s free.

Great exercises

[Catherine Liu · Rating 4 out of 5]

i actually only read up until metric spaces but i deserve to log this as read