Mathematical Analysis I

by Elias Zakon

Description: This award-winning text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material.

For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.

Mathematical Analysis II completes this series with material on measure and integration and calculus on normed linear spaces.

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Audience: This text is appropriate for any undergraduate mathematics course in real analysis or mathematical analysis, or for a preparatory class for beginning mathematics graduate students who will later advance to courses in measure theory and functional analysis. Knowledge of this material will also be of benefit to graduate students in economics, signal and image processing, fluid and structural mechanics, etc.

Publishing Information: Mathematical Analysis I, by Elias Zakon, ISBN 978-1-931705-02-X, published by The Trillia Group, 2004. 355+xii pages, 554 exercises, 26 figures, hypertextual cross-references, hyperlinked index of terms. Download size: 2088 to 2298 KB, depending on format. Current version released May 18, 2017.

Print Edition: Proceedings.com reprints Mathematical Analysis I in paperback format on acid-free paper; you can order the paperback edition (ISBN 978-1-61738-647-3, US$30) from their website.

South Asia Edition: Overseas Press India Pvt. Ltd. offers a print edition of Mathematical Analysis I (ISBN 978-81-88689-467, 395 Indian rupees) for distribution mainly in South Asia, specifically, India, Pakistan, Sri Lanka, Bangladesh, Nepal, Bhutan, Myanmar, and the Maldives.

Excerpts from the Text: The Preface, the Table of Contents, and the Index.

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Errata: There is a list of errata that records changes made to the text since the version of May 20, 2004. The latest version of the book is always available at the links above.