Mathematical Analysis I
by Elias Zakon
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.
Download the Book: The book is available in a number of formats; click below on the format you would like.|
- Larger print, one page per sheet of paper, bind at left.
- Regular print, two pages per sheet of paper, bind at top.
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.
Recognition and Reviews:
Recognition and reviews of Mathematical Analysis I are noted here.
You can add your own review of this book at The Assayer.
Terms and Conditions: Thanks to funding from the Saylor Foundations's Open Textbook Challenge, this text is distributed under a Creative Commons Attribution 3.0 Unported (CC BY 3.0) license. Use and distribution of this text is allowed as long as the copyright notice and attribution statement are maintained with the book. (This is a paraphrase of part of the license, see the complete license terms in case of any questions.)
Site Licenses: Because this book is licensed under a Creative Commons Attribution 3.0 Unported (CC BY 3.0) license, any campus can use this book as a text without buying a
Check our list of site licenses to see whether you are a member
of a group that has purchased a site license
for one of our other texts.
Donate: The Trillia Group accepts donations from people who are otherwise licensed to use Mathematical Analysis I free of charge.
Donations of as little as US$2 or €2 help us continue to produce and distribute quality online texts.
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.