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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. In addition, the notes include many carefully selected exercises of various levels of difficulty. Hints and solutions to selected exercises are available in the back of the book. For each section, there is at least one exercise with hints or fully solved. For those exercises, besides the solutions, there are explanations about the process itself and examples of more general problems where the same technique may be used.

The last chapter contains additional topics. These include topological properties of the real line, generalizations of the extreme value theorem and more contemporary topics that expand on the notions of continuity or optimization. Lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects.

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DOI

10.15760/pdxopen-34

Publication Date

9-2022

Publisher

Portland State University Library

City

Portland

Subjects

Mathematical analysis -- Foundations, Mathematics

Rights

© 2022 Beatriz Lafferriere, Gerardo Lafferriere, and Mau Nam Nguyen

Creative Commons License
This open access textbook is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Notes

This third 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.

Editions and funding
This open textbook was originally published in 2016

The first edition can be found here: http://archives.pdx.edu/ds/psu/13067

The second edition can be found here: https://doi.org/10.15760/pdxopen-9

Publication of this book was made possible by Portland State University Library PDXOpen Publishing Initiative Grant program. Published by Portland State University Library.

Persistent Identifier

https://archives.pdx.edu/ds/psu/38545

Introduction to Mathematical Analysis I - 3rd Edition

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