A First Course In Analysis
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A First Course In Analysis
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Author : George Pedrick
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-10
A First Course In Analysis written by George Pedrick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-10 with Mathematics categories.
The first course in Analysis, which follows calculus, along with other courses, such as differential equations and elementary linear algebra, in the curricu lum, presents special pedagogical challenges. There is a change of stress from computational manipulation to "proof. " Indeed, the course can become more a course in Logic than one in Analysis. Many students, caught short by a weak command of the means of mathematical discourse and unsure of what is expected of them, what "the game" is, suffer bouts of a kind of mental paralysis. This text attempts to address these problems in several ways: First, we have attempted to define "the game" as that of "inquiry," by using a form of exposition that begins with a question and proceeds to analyze, ultimately to answer it, bringing in definitions, arguments, conjectures, exam ples, etc. , as they arise naturally in the course of a narrative discussion of the question. (The true, historical narrative is too convoluted to serve for first explanations, so no attempt at historical accuracy has been made; our narra tives are completely contrived. ) Second, we have kept the logic informal, especially in the course of preliminary speculative discussions, where common sense and plausibility tempered by mild skepticism-serve to energize the inquiry.
A First Course In Real Analysis
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Author : Sterling K. Berberian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-10
A First Course In Real Analysis written by Sterling K. Berberian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-10 with Mathematics categories.
Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along theway, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.
A First Course In Analysis
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Author : Donald Yau
language : en
Publisher: World Scientific
Release Date : 2013
A First Course In Analysis written by Donald Yau and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
This book is an introductory text on real analysis for undergraduate students. The prerequisite for this book is a solid background in freshman calculus in one variable. The intended audience of this book includes undergraduate mathematics majors and students from other disciplines who use real analysis. Since this book is aimed at students who do not have much prior experience with proofs, the pace is slower in earlier chapters than in later chapters. There are hundreds of exercises, and hints for some of them are included.
A First Course In Real Analysis
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Author : M.H. Protter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A First Course In Real Analysis written by M.H. Protter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.
A First Course In Functional Analysis
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Author : Martin Davis
language : en
Publisher: Courier Corporation
Release Date : 2013-01-01
A First Course In Functional Analysis written by Martin Davis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
Designed for undergraduate mathematics majors, this introductory treatment is based on the distinguished author's lecture notes. The self-contained exposition of Gelfand's proof of Wiener's theorem explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and analytic functions into a Banach space. 1966 edition.
A First Course In Numerical Analysis
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Author : Anthony Ralston
language : en
Publisher: Courier Corporation
Release Date : 2001-01-01
A First Course In Numerical Analysis written by Anthony Ralston and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.
A First Course In Functional Analysis
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Author : Rabindranath Sen
language : en
Publisher: Anthem Press
Release Date : 2014-11-01
A First Course In Functional Analysis written by Rabindranath Sen and has been published by Anthem Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-01 with Mathematics categories.
This book provides the reader with a comprehensive introduction to functional analysis. Topics include normed linear and Hilbert spaces, the Hahn-Banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the Lebesgue measure. The book explains the motivation for the development of these theories, and applications that illustrate the theories in action. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘A First Course in Functional Analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering.
A First Course In Factor Analysis
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Author : Andrew L. Comrey
language : en
Publisher: Psychology Press
Release Date : 2013-11-12
A First Course In Factor Analysis written by Andrew L. Comrey and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-12 with Psychology categories.
The goal of this book is to foster a basic understanding of factor analytic techniques so that readers can use them in their own research and critically evaluate their use by other researchers. Both the underlying theory and correct application are emphasized. The theory is presented through the mathematical basis of the most common factor analytic models and several methods used in factor analysis. On the application side, considerable attention is given to the extraction problem, the rotation problem, and the interpretation of factor analytic results. Hence, readers are given a background of understanding in the the theory underlying factor analysis and then taken through the steps in executing a proper analysis -- from the initial problem of design through choice of correlation coefficient, factor extraction, factor rotation, factor interpretation, and writing up results. This revised edition includes introductions to newer methods -- such as confirmatory factor analysis and structural equation modeling -- that have revolutionized factor analysis in recent years. To help remove some of the mystery underlying these newer, more complex methods, the introductory examples utilize EQS and LISREL. Updated material relating to the validation of the Comrey Personality Scales also has been added. Finally, program disks for running factor analyses on either an IBM-compatible PC or a mainframe with FORTRAN capabilities are available. The intended audience for this volume includes talented but mathematically unsophisticated advanced undergraduates, graduate students, and research workers seeking to acquire a basic understanding of the principles supporting factor analysis. Disks are available in 5.25" and 3.5" formats for both mainframe programs written in Fortran and IBM PCs and compatibles running a math co-processor.
A Companion To Analysis
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Author : Thomas William Körner
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
A Companion To Analysis written by Thomas William Körner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician. Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique.
A First Course In Harmonic Analysis
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Author : Anton Deitmar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A First Course In Harmonic Analysis written by Anton Deitmar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
This book is intended as a primer in harmonic analysis at the un dergraduate level. All the central concepts of harmonic analysis are introduced without too much technical overload. For example, the book is based entirely on the Riemann integral instead of the more demanding Lebesgue integral. Furthermore, all topological questions are dealt with purely in the context of metric spaces. It is quite sur prising that this works. Indeed, it turns out that the central concepts theory can be explained using very little of this beautiful and useful technical background. The first aim of this book is to give a lean introduction to Fourier analysis, leading up to the Poisson summation formula. The sec ond aim is to make the reader aware of the fact that both principal incarnations of Fourier Theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The third goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.