Real mathematical analysis (Record no. 204360)

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fixed length control field 02689 a2200229 4500
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fixed length control field 160816b2015 xxu||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783319177700
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515
Item number P8R3-2015
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Pugh, Charles C.
9 (RLIN) 335555
245 ## - TITLE STATEMENT
Title Real mathematical analysis
250 ## - EDITION STATEMENT
Edition statement 2nd ed
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Name of publisher, distributor, etc Springer
Date of publication, distribution, etc 2015
Place of publication, distribution, etc New York
300 ## - PHYSICAL DESCRIPTION
Extent xi, 478 p.
440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE
Title Undergraduate Texts in Mathematics
9 (RLIN) 335556
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Table of Contents:

Chapter I Real Numbers

Chapter II A Taste of Topology

Chapter III Functions of a Real Variable

Chapter IV Function Spaces

Chapter V Multivariable Calculus

Chapter VI Lebesgue Theory

520 ## - SUMMARY, ETC.
Summary, etc 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 under graph 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.

(http://www.springer.com/gp/book/9783319177700#aboutBook)
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematical analysis
9 (RLIN) 661
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics - Real numbers - Topology
9 (RLIN) 335557
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Functions - Real variables
9 (RLIN) 335558
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Multivariable calculus - Lebesgue theory - Exercises
9 (RLIN) 335559
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Item type Books
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Collection code Permanent location Current location Shelving location Date acquired Source of acquisition Cost, normal purchase price Item location Total Checkouts Total Renewals Full call number Barcode Date last seen Date last borrowed Cost, replacement price Koha item type
          Non-fiction Vikram Sarabhai Library Vikram Sarabhai Library   2016-08-04 12 2825.37 Slot 1373 (0 Floor, East Wing) 3 5 515 P8R3-2015 192630 2019-10-15 2019-09-03 3531.72 Books

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