Real Mathematical Analysis

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Características del artículo

Estado
Nuevo: Libro nuevo, sin usar y sin leer, que está en perfecto estado; incluye todas las páginas sin ...
Country of Origin
United States
Educational Level
Adult & Further Education
Personalized
No
Level
Advanced
ISBN
9783319330426
Categoría

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Product Identifiers

Publisher
Springer International Publishing A&G
ISBN-10
331933042X
ISBN-13
9783319330426
eBay Product ID (ePID)
15038412862

Product Key Features

Number of Pages
Xi, 478 Pages
Language
English
Publication Name
Real Mathematical Analysis
Publication Year
2016
Subject
Mathematical Analysis
Type
Textbook
Author
Charles C. Pugh
Subject Area
Mathematics
Series
Undergraduate Texts in Mathematics Ser.
Format
Trade Paperback

Dimensions

Item Height
1 in
Item Weight
322.7 Oz
Item Length
10 in
Item Width
7 in

Additional Product Features

Edition Number
2
Intended Audience
Trade
Reviews
"This book, in its second edition, provides thebasic concepts of real analysis. ... I strongly recommend it to everyone whowishes to study real mathematical analysis." (Cătălin Barbu, zbMATH 1329.26003,2016), This book, in its second edition, provides the basic concepts of real analysis. I strongly recommend it to everyone who wishes to study real mathematical analysis. (C t lin Barbu, zbMATH 1329.26003, 2016) "
Dewey Edition
22
Number of Volumes
1 vol.
Illustrated
Yes
Original Language
English
Dewey Decimal
515
Table Of Content
Real Numbers.- A Taste of Topology.- Functions of a Real Variable.- Function Spaces.- Multivariable Calculus.- Lebesgue Theory.
Synopsis
Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis.New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the undergraph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line/one-picture proof of Fubini's theorem from Cavalieri's Principle, and, in many cases, the ability to see an integral result from measure theory. The presentation includes Vitali's Covering Lemma, density points -- which are rarely treated in books at this level -- and the almost everywhere differentiability of monotone functions. Several new exercises now join a collection of over 500 exercises that pose interesting challenges and introduce special topics to the student keen on mastering this beautiful subject., Elucidates abstract concepts and salient points in proofs with over 150 detailed illustrations Treats the rigorous foundations of both single and multivariable Calculus Gives an intuitive presentation of Lebesgue integration using the undergraph approach of Burkill Includes over 500 exercises that are interesting and thought-provoking, not merely routine
LC Classification Number
QA312-312.5

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