http://www.merlot.org:80/merlot/ A search of MERLOT materials Copyright 1997-2013 MERLOT. All rights reserved. Tue, 21 May 2013 04:59:19 PDT Tue, 21 May 2013 04:59:19 PDT http://www.merlot.org:80/merlot/images/merlot.gif http://www.merlot.org:80/merlot/ 44 34 http://www.merlot.org/merlot/viewMaterial.htm?id=437407 This is a free, online textbook that is also part of an online course. According to the author, "Analysis is the study of limits. Anything in mathematics which has limits in it uses ideas of analysis. Some of the examples which will be important in this course are sequences, infinite series, derivatives of functions, and integrals. As you know from calculus, limits are the basis of understanding integration and differentiation, and, as you also know from calculus, these things are the basis of everything in the world you could ever need to know.״ http://www.merlot.org/merlot/viewMaterial.htm?id=518850 According to OER Commons, 'These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated "from scratch." This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.' http://www.merlot.org/merlot/viewMaterial.htm?id=437630 This is a free, online textbook for an introductory course in complex analysis. General topics include Complex Numbers, Complex Functions, Elementary Functions, Integration, Cauchy's Theorem, More Integration, Harmonic Functions, Series, Taylor and Laurent Series, Poles, Residues, and All That, and Argument Principle. Each chapter from the book can be downloaded as a free pdf file. http://www.merlot.org/merlot/viewMaterial.htm?id=513199 This is a free, online textbook offered by Bookboon.com. Topics include: 1. Some necessary theoretical results, 2. Polynomials, 3. Fractional functions, 4. The exponential function and the logarithm function, 5. Trigonometric and hyperbolic functions, and 6. Harmonic functions. http://www.merlot.org/merlot/viewMaterial.htm?id=513201 This is a free, online textbook offered by Bookboon.com. Topics include: 1. Some simple theoretical results concerning power series, 2. Simple Fourier series in the Theory of Complex Functions, 3. Power series, 4. Analytic functions described as power series, 5. Linear differential equations and the power series method, 6. The classical differential equations, 7. Some more difficult differential equations, 8. Zeros of analytic functions, 9. Fourier series, and 10. The maximum principle. http://www.merlot.org/merlot/viewMaterial.htm?id=513203 This is a free, online textbook offered by Bookboon.com. "This is the fifth textbook you can download for free containing examples from the Theory of Complex Functions. In this volume we shall consider the Laurent series and their relationship to the general theory, and finally the technique of solving linear differential equations with polynomial coefficients by means of Laurent series.״ 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 mathematicsmajors and science students with a serious interest in mathematics. Prospectiveeducators or mathematically gifted high school students can also benefit from the mathematicalmaturity 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 usuallypresented in an elementary course, and to provide the background required for insight intomore advanced courses in pure and applied mathematics. The standard elementary calculussequence is the only specific prerequisite for Chapters 1–5, which deal with real-valuedfunctions. (However, other analysis oriented courses, such as elementary differential equation,also provide useful preparatory experience.) Chapters 6 and 7 require a workingknowledge of determinants, matrices and linear transformations, typically available from afirst course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5." http://www.merlot.org/merlot/viewMaterial.htm?id=447163 This is a free, online textbook. According to the author, "This 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.״ http://www.merlot.org/merlot/viewMaterial.htm?id=437635 This is a free, online textbook that addresses the following topics: Chapter 1: Geometry of Rn, Functions from R to Rn, Functions from Rn to R, and Functions from Rm to Rn 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, "