東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Real mathematical analysis

Pugh, Charles C.

Linked to FindBook

Google Book

Amazon

博客來

Real mathematical analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Real mathematical analysis/ by Charles C. Pugh.
Author:	Pugh, Charles C.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xi, 478 p. :ill., digital ;24 cm.
[NT 15003449]:	Real Numbers -- A Taste of Topology -- Functions of a Real Variable -- Function Spaces -- Multivariable Calculus -- Lebesgue Theory.
Contained By:	Springer eBooks
Subject:	Mathematical analysis. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-17771-7
ISBN:	9783319177717 (electronic bk.)

Real mathematical analysis
Pugh, Charles C.

Real mathematical analysis[electronic resource] /by Charles C. Pugh. - 2nd ed. - Cham :Springer International Publishing :2015. - xi, 478 p. :ill., digital ;24 cm. - Undergraduate texts in mathematics,0172-6056. - Undergraduate texts in mathematics..

Real Numbers -- A Taste of Topology -- Functions of a Real Variable -- Function Spaces -- Multivariable Calculus -- Lebesgue Theory.

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, Dieudonne, 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.

ISBN: 9783319177717 (electronic bk.)

Standard No.: 10.1007/978-3-319-17771-7doiSubjects--Topical Terms:

516833
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

Real mathematical analysis
LDR:02790nmm a2200337 a 4500 001 2009095
003 DE-He213
005 20160223105110.0
006 m d
007 cr nn 008maaau
008 160311s2015 gw s 0 eng d
020 $a 9783319177717 (electronic bk.)
020 $a 9783319177700 (paper)
024 7 $a 10.1007/978-3-319-17771-7 $2 doi
035 $a 978-3-319-17771-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA300
072 7 $a PBKL $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515 $2 23
090 $a QA300 $b .P978 2015
100 1 $a Pugh, Charles C. $3 2157942
245 1 0 $a Real mathematical analysis $h [electronic resource] / $c by Charles C. Pugh.
250 $a 2nd ed.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xi, 478 p. : $b ill., digital ; $c 24 cm.
490 1 $a Undergraduate texts in mathematics, $x 0172-6056
505 0 $a Real Numbers -- A Taste of Topology -- Functions of a Real Variable -- Function Spaces -- Multivariable Calculus -- Lebesgue Theory.
520 $a 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, Dieudonne, 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.
650 0 $a Mathematical analysis. $3 516833
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Measure and Integration. $3 891263
650 2 4 $a Real Functions. $3 891265
650 2 4 $a Sequences, Series, Summability. $3 897266
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Undergraduate texts in mathematics. $3 1041596
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-17771-7
950 $a Mathematics and Statistics (Springer-11649)