Files
Download Full Text (1.8 MB)
Description
Video lectures explaining problem solving strategies are available
Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.
The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.
The second edition includes a number of improvements based on recommendations from students and colleagues and on our own experience teaching the course over the last several years.
In this edition we streamlined the narrative in several sections, added more proofs, many examples worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts).
Adopt/Adapt
If you are an instructor adopting or adapting this PDXOpen textbook, please help us understand your use by filling out this form
DOI
10.15760/pdxopen-9
Publication Date
12-2016
Publisher
Portland State University Library
City
Portland
Subjects
Mathematical analysis -- Foundations, Mathematics
Rights
© 2018 Beatriz Lafferriere, Gerardo Lafferriere, and Nguyen Mau Nam
This open access textbook is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Persistent Identifier
http://archives.pdx.edu/ds/psu/18747
Recommended Citation
Lafferriere, Beatriz; Lafferriere, Gerardo; and Nguyen, Mau Nam, "Introduction to Mathematical Analysis I - 2nd Edition" (2016). PDXOpen: Open Educational Resources. 12.
https://pdxscholar.library.pdx.edu/pdxopen/12
10.15760/pdxopen-9
Notes
This open textbook was originally published in 2016
The third edition can be found here:https://archives.pdx.edu/ds/psu/38545
The first edition can be found here: http://archives.pdx.edu/ds/psu/13067
Publication of this book was made possible by Portland State University Library PDXOpen Publishing Initiative Grant program. Published by Portland State University Library.