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-1-1Interactive Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=85542
<p>Quoted from the site: "Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, and more."</p>Thu, 05 Jan 2006 08:00:00 GMTWachsmuth, Bert G. Seton Hall UniversityA Short Course in Information Theory
https://www.merlot.org/merlot/viewMaterial.htm?id=89011
A Short Course in Information Theory.Tue, 08 May 2001 07:00:00 GMTDavid J.C. MacKay Cavendish Laboratory, CambridgeA Primer of Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=1325156
<p>This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.</p>Thu, 24 Aug 2017 14:27:38 GMTDan Sloughter Furman UniversityElementary Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=905925
<p>'This book is the second edition of an undergraduate level Real Analysis textbook formerly published by Prentice Hall (Pearson) in 2001.</p>
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<div>It is designed to be a user-friendly text that is suitable for a one year course.</div>
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<div>Additional elementary material designated as<em>enrichment</em> can be included for students with minimal background. Material designated as<em>advanced</em> is intended for students with stronger backgrounds. Such topics are of a more sophisticated nature.</div>
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<div>The text consists of two volumes, each covering a semester course.'</div>
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https://www.merlot.org/merlot/viewMaterial.htm?id=1071171
<p>The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.</p>
<p>This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context.</p>
<p>This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.</p>Wed, 14 Oct 2015 16:45:36 GMTRobert Rogers; Eugene Boman State University of New York at Fredonia; The Pennsylvania State University, HarrisburgIntroduction to Mathematical Analysis I
https://www.merlot.org/merlot/viewMaterial.htm?id=1325312
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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).</p>Thu, 24 Aug 2017 19:53:23 GMTBeatriz Lafferriere; Gerardo Lafferriere; Mau Nam Nguyen Portland State University; Portland State University; Portland State UniversityReal Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=905913
<p>'This book is the second edition of a graduate level real analysis textbook formerly published by Prentice Hall (Pearson) in 1997. This edition contains many corrections, additions and is in a new format. </p>
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<div> It is designed to be user-friendly by including historical material, by giving examples to motivate topics before they are developed, and by providing motivation for the proofs of theorems that students often find difficult. </div>
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<div>The text consists of two volumes, each covering a semester course.</div>
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<div>More about the goals and use of the book can be found in the <a href="http://www.classicalrealanalysis.info/com/BBT-Preface.php">Preface</a>. See also the <a href="http://www.classicalrealanalysis.info/com/BBT-TableOfContents.php">Table of Contents</a>, which lists the topics covered in each volume. ' </div>Tue, 04 Nov 2014 02:04:53 GMTBrian S. Thomson; Judith B. Bruckner; Andrew M. BrucknerThe Calculus Integral
https://www.merlot.org/merlot/viewMaterial.htm?id=905932
<p>'An elementary introduction to integration theory on the real line. This is at the level of an honor's course in calculus or a first undergraduate level real analysis course. In the end the student should be adequately prepared for a graduate level course in Lebesgue integration.</p>
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<div><span style="font-family: Arial;">Read the <span style="color: #cc0000;"><a title="" href="http://www.classicalrealanalysis.info/com/TCI-Preface.php">Preface</a></span> and browse through the<span style="color: #cc0000;"><a title="" href="http://www.classicalrealanalysis.info/com/TCI-TableOfContents.php">Table of Contents</a></span>. </span></div>Tue, 04 Nov 2014 02:21:17 GMTBrian S. ThomsonApplication of six sigma in Quality
https://www.merlot.org/merlot/viewMaterial.htm?id=79064
Talking about quality it is producing better with less waste of money and time. Applying the six sigma can help to reduce cost of production. Through this web anybody can apply to become menber of ASQ, for training and take online courses about quality and the updating of ISO 9000.Fri, 28 Mar 2003 08:00:00 GMTGureline dumeFUNCTIONS DEFINED BY IMPROPER INTEGRALS
https://www.merlot.org/merlot/viewMaterial.htm?id=826915
<p>'This is a supplement to the author’s Introduction to Real Analysis. It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute’s Open Textbook Initiative. It may be copied, modiﬁed, redistributed, translated, and built upon subject to the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. A complete instructor’s solution manual is available by email to wtrench@trinity.edu, subject to veriﬁcation of the requestor’s faculty status.'</p><p>Introduction to Real Analysis: <a href="viewMaterial.htm?id=516759" target="_blank">http://www.merlot.org/merlot/viewMaterial.htm?id=516759</a></p><p> <span>NOTE: This book meets the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Open Textbook Initiative. </span><a tabindex="-1" href="http://www.aimath.org/textbooks/" target="_parent">http://www.aimath.org/textbooks/</a></p>Wed, 15 Jan 2014 22:26:27 GMTWilliam Trench Trinity UniversityThe Method of Lagrange Multipliers
https://www.merlot.org/merlot/viewMaterial.htm?id=826948
<p>This is a supplement to the author’s Introduction to Real Analysis. It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute’s Open Textbook Initiative. It may be copied, modiﬁed, redistributed, translated, and built upon subject to the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. A complete instructor’s solution manual is available by email to wtrench@trinity.edu, subject to veriﬁcation of the requestor’s faculty status.</p><p>Introduction to Real Analysis: <a href="viewMaterial.htm?id=516759" target="_blank">http://www.merlot.org/merlot/viewMaterial.htm?id=516759</a></p><p> </p>Wed, 15 Jan 2014 22:32:04 GMTWilliam Trench Trinity UniversityHow We Got from There to Here: A Story of Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=1221225
<p>The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.</p>
<p>This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context.</p>
<p>This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.</p>Fri, 12 Aug 2016 01:25:34 GMTRobert Rogers; Eugene Boman State University of New York; The Pennsylvania State UniversityIntroduction to Mathematical Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=1221235
<p>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.</p>
<p>The textbook 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.</p>Fri, 12 Aug 2016 01:33:38 GMTBeatriz Lafferriere; Gerardo Lafferriere; Mau Nam Nguyen Portland State University; Portland State University; Portland State UniversityIntroduction To Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=516759
<p>"This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5."</p><p><span>NOTE: This book meets the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Open Textbook Initiative. </span><a tabindex="-1" href="http://www.aimath.org/textbooks/" target="_parent">http://www.aimath.org/textbooks/</a></p>Tue, 25 Jan 2011 22:19:47 GMTWilliam Trench Trinity UniversityReal Analysis I
https://www.merlot.org/merlot/viewMaterial.htm?id=620155
This course is designed to introduce the student to the rigorous examination of the real number system and the foundations of calculus. Analysis lies at the heart of the trinity of higher mathematics—algebra, analysis, and topology—because it is where the other two fields meet. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 241)Fri, 27 Jan 2012 18:52:43 GMTThe Saylor FoundationReal Functions in Several Variables: Volume XI Vector Fields II
https://www.merlot.org/merlot/viewMaterial.htm?id=1247136
<p>This is a free textbook offered by BookBoon.</p>
<p>The topic of this series of books on "Real Functions in Several Variables" is very important in the description in e.g. Mechanics of the real 3-dimensional world that we live in. Therefore, we start from the beginning, modelling this world by using the coordinates of R3 to describe e.b. a motion in space.</p>
<p>The theory and methods of these volumes on "Real Functions in Several Variables" are applied constantly in higher Mathematics, Mechanics and Engineering Sciences. It is of paramount importance for the calculations in Probability Theory, where one constantly integrate over some point set in space.</p>
<p>It is my hope that this text, these guidelines and these examples, of which many are treated in more ways to show that the solutions procedures are not unique, may be of some inspiration for the students who have just started their studies at the universities.</p>Mon, 07 Nov 2016 22:11:33 GMTLeif MejlbroTheory of functions of a real variable
https://www.merlot.org/merlot/viewMaterial.htm?id=518988
<p>AccoI have taught the beginning graduate course in real variables and functional analysis three times in the last five years, and this book is the result. The course assumes that the student has seen the basics of real variable theory and point set topology. The elements of the topology of metrics spaces are presented (in the nature of a rapid review) in Chapter I. The course itself consists of two parts: 1) measure theory and integration, and 2) Hilbert space theory, especially the spectral theorem and its applications. In Chapter II I do the basics of Hilbert space theory, i.e. what I can do without measure theory or the Lebesgue integral. The hero here (and perhaps for the first half of the course) is the Riesz representation theorem. Included is the spectral theorem for compact self-adjoint operators and applications of this theorem to elliptic partial di erential equations. Chapter III is a rapid presentation of the basics about the Fourier transform. Chapter IV is concerned with measure theory."rding to the author, "</p>Wed, 02 Feb 2011 23:01:45 GMTShlomo Sternberg Harvard Psychology