# Introduction to Mathematical Analysis I - Second Edition

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Beatriz Lafferriere, Portland State University

Gerardo Lafferriere, Portland State University

Mau Nam Nguyen, Portland State University

ISBN 13: 9781365605529

Publisher: Portland State University Library

Language: English

## Conditions of Use

CC BY-NC

• 1 Tools for Analysis
• 2 Sequences
• 3 Limits and Continuity
• 4 Differentiation
• 5 Solutions and Hints for Selected Exercises

## Ancillary Material

• Portland State University Library

Our goal with this textbook 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).

### Authors

Beatriz Lafferriere, Assistant Professor, Fariborz Maseeh Department of Mathematics and Statistics, Assistant Chair for Undergraduate Program, Director of Undergraduate Advising, Portland State University. PhD Rutgers University.

Gerardo Lafferriere, Professor, Fariborz Maseeh Department of Mathematics and Statistics, Portland State University. PhD Rutgers University. Area of Specialty: Mathematical Control Theory, Hybrid Systems, Mathematical Biology, Robotics

Mau Nam Nguyen, Associate Professor, Fariborz Maseeh Department of Mathematics and Statistics, Portland State University. Ph.D. 2007 Wayne State University. Area of Specialty: Variational & Convex Analysis, Mathematical Optimization, Non-Linear & Functional Analysis.