Welcome to The Trillia Group
• Basic Concepts of Mathematics
• Mathematical Analysis I
• Mathematical Analysis II
• An Introduction to the Theory of Numbers
Online Math
Privacy Policy
Site Map
About Trillia
Mathematical Analysis I, by Elias Zakon
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.

Download the Book: The book is available in a number of formats; click below on the format you would like. You will need Adobe Acrobat Reader or another program that can work with Portable Document Format (PDF) files to display or print the book. Note: If you have difficulties reading our products with Adobe Acrobat Reader, please consult this page to see whether we have already been able to diagnose and solve the difficulty you are having.

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.

This text covers similar material to the books (we give US list prices for current hardcover editions at Amazon on July 10, 2006): Principles of Mathematical Analysis by W. Rudin ($130.00); Introductory Real Analysis by F. D'Angelo and M. Seyfried ($137.56); Introduction to Real Analysis by R. Bartle and D. Sherbert ($125.95); Real Analysis by H. Royden ($124.80); Introduction to Real Analysis by W. Trench ($114.40), etc. (Updated January 13, 2010: Introduction to Metric and Topological Spaces by Wilson A. Sutherland ($85.00 hardcover, $35.04 paperback); Elementary Real Analysis by B. S. Thomson, J. B. Bruckner, and A. M. Bruckner ($26.95 paperback).)

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 July 6, 2011.

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 site license. 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.

Copyright © 2001-2015 by The Trillia Group.
The phrase "The Trillia Group" and The Trillia Group logo are trademarks of The Trillia Group.
The Trillia Group participates in the eGranary Digital Library initiative of the WiderNet Project.