Introduction to Mathematical Analysis I

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, thes...

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Main Authors: Lafferriere, Beatriz (Author), Lafferriere, Gerardo (Author), Nguyen, Mau Nam (Author)
Format: Electronic eBook
Language:English
Published: [Place of publication not identified] Portland State University Library [2016]
Edition:Second Edition
Series:Open textbook library.
Subjects:
Online Access:Access online version
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100 1 |a Lafferriere, Beatriz  |e author 
245 0 0 |a Introduction to Mathematical Analysis I  |c Beatriz Lafferriere 
250 |a Second Edition 
264 2 |a Minneapolis, MN  |b Open Textbook Library 
264 1 |a [Place of publication not identified]  |b Portland State University Library  |c [2016] 
264 4 |c ©2016. 
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505 0 |a 1 Tools for Analysis -- 2 Sequences -- 3 Limits and Continuity -- 4 Differentiation -- 5 Solutions and Hints for Selected Exercises 
520 0 |a 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). 
542 1 |f Attribution-NonCommercial 
546 |a In English. 
588 0 |a Description based on online resource 
650 0 |a Mathematics  |v Textbooks 
650 0 |a Applied mathematics  |v Textbooks 
650 0 |a Analysis  |v Textbooks 
700 1 |a Lafferriere, Gerardo  |e author 
700 1 |a Nguyen, Mau Nam  |e author 
710 2 |a Open Textbook Library  |e distributor 
856 4 0 |u https://open.umn.edu/opentextbooks/textbooks/243  |z Access online version