Real mathematical analysis [electronic resource] / Charles Chapman Pugh.
2015
QA300
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Details
Title
Real mathematical analysis [electronic resource] / Charles Chapman Pugh.
Edition
Second edition.
ISBN
9783319177717 electronic book
3319177710 electronic book
9783319177700
3319177710 electronic book
9783319177700
Published
Cham : Springer, 2015.
Language
English
Description
1 online resource (xi, 478 pages) : illustrations.
Item Number
10.1007/978-3-319-17771-7 doi
Call Number
QA300
Dewey Decimal Classification
515
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed August 5, 2015).
Series
Undergraduate texts in mathematics.
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Record Appears in
Table of Contents
Real Numbers
A Taste of Topology
Functions of a Real Variable
Function Spaces
Multivariable Calculus
Lebesgue Theory.
A Taste of Topology
Functions of a Real Variable
Function Spaces
Multivariable Calculus
Lebesgue Theory.