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4434Elementary Real Analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=905925
'This book is the second edition of an undergraduate level Real Analysis textbook formerly published by Prentice Hall (Pearson) in 2001. It is designed to be a user-friendly text that is suitable for a one year course. Additional elementary material designated asenrichment can be included for students with minimal background. Material designated asadvanced is intended for students with stronger backgrounds. Such topics are of a more sophisticated nature. The text consists of two volumes, each covering a semester course.'FUNCTIONS DEFINED BY IMPROPER INTEGRALS
http://www.merlot.org/merlot/viewMaterial.htm?id=826915
'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.'Introduction to Real Analysis: http://www.merlot.org/merlot/viewMaterial.htm?id=516759 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. http://www.aimath.org/textbooks/Introduction To Real Analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=516759
״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.״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. http://www.aimath.org/textbooks/Real Analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=905913
'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. 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. The text consists of two volumes, each covering a semester course. More about the goals and use of the book can be found in the Preface. See also the Table of Contents, which lists the topics covered in each volume. ' The Calculus Integral
http://www.merlot.org/merlot/viewMaterial.htm?id=905932
'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. Read the Preface and browse through theTable of Contents. The Method of Lagrange Multipliers
http://www.merlot.org/merlot/viewMaterial.htm?id=826948
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.Introduction to Real Analysis: http://www.merlot.org/merlot/viewMaterial.htm?id=516759 Theory of functions of a real variable
http://www.merlot.org/merlot/viewMaterial.htm?id=518988
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, "