Author : G. B. Folland
Publisher : American Mathematical Soc.
Page : 107 pages
File Size : 34,39 MB
Release : 2014-05-14
Category : Education
ISBN : 0883859157
A concise guide to the core material in a graduate level real analysis course.
Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 12,64 MB
Release : 2008-07-11
Category : Mathematics
ISBN : 0817644423
* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
Author : N. L. Carothers
Publisher : Cambridge University Press
Page : 420 pages
File Size : 25,89 MB
Release : 2000-08-15
Category : Mathematics
ISBN : 9780521497565
A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.
Author : Sterling K. Berberian
Publisher : Springer Science & Business Media
Page : 249 pages
File Size : 28,86 MB
Release : 2012-09-10
Category : Mathematics
ISBN : 1441985484
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 the way, (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.
Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 671 pages
File Size : 16,36 MB
Release : 2007-10-04
Category : Mathematics
ISBN : 0817644415
Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.
Author : Terence Tao
Publisher : Springer
Page : 366 pages
File Size : 10,53 MB
Release : 2016-08-29
Category : Mathematics
ISBN : 9811017891
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
Author : Patrick Fitzpatrick
Publisher : American Mathematical Soc.
Page : 610 pages
File Size : 21,24 MB
Release : 2009
Category : Mathematics
ISBN : 0821847910
"Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."--pub. desc.
Author : Gerald B. Folland
Publisher : John Wiley & Sons
Page : 368 pages
File Size : 14,65 MB
Release : 2013-06-11
Category : Mathematics
ISBN : 1118626397
An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.
Author : Robert S. Borden
Publisher : Courier Corporation
Page : 421 pages
File Size : 15,91 MB
Release : 2012-09-11
Category : Mathematics
ISBN : 0486150380
This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more. Carefully chosen problems appear at the end of each chapter, and this new edition features an additional appendix of tips and solutions for selected problems.
Author : Kenneth A. Ross
Publisher : CUP Archive
Page : 192 pages
File Size : 47,75 MB
Release : 2014-01-15
Category : Mathematics
ISBN :
