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Description
Video lectures explaining problem solving strategies are available.
This set of lecture notes is meant 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.
Introduction to Mathematical Analysis II contains lecture notes that complement this book, with sections on integration, numerical series, series of functions, and selected advanced topics. Together, both volumes support a one semester or two-quarter course on introductory mathematical analysis.
Introduction to Mathematical Analysis I contains 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
This open access textbook is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Persistent Identifier
https://archives.pdx.edu/ds/psu/38545
Recommended Citation
Lafferriere, Beatriz; Lafferriere, Gerardo; and Nguyen, Mau Nam, "Introduction to Mathematical Analysis I - 3rd Edition" (2022). PDXOpen: Open Educational Resources.
DOI: https://doi.org/10.15760/pdxopen-34
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
Previous editions of Introduction to Mathematical Analysis I, Third Edition, include:
Introduction to Mathematical Analysis I, First Edition
Introduction to Mathematical Analysis I, Second Edition
Publication of this book was made possible by Portland State University Library PDXOpen Publishing Initiative Grant program.