عنوان

Real mathematical analysis /

شابک

3319177710

شابک

9783319177717

شابک اشتباه

9783319177700

شماره

dltt

عنوان اصلي

Real mathematical analysis /

نام عام مواد

[Book]

نام نخستين پديدآور

Charles Chapman Pugh

وضعيت ويراست

Second edition

وضعيت ويراست

Second edition

نام خاص و کميت اثر

1 online resource (xi, 478 pages) :

ساير جزييات

illustrations.

عنوان فروست

Undergraduate texts in mathematics

متن يادداشت

Includes bibliographical references and index

متن يادداشت

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

بدون عنوان

0

متن يادداشت

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

موضوع مستند نشده

Mathematical analysis.

موضوع مستند نشده

QA

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Pugh, C. C., (Charles Chapman),1940-

مستند نام تنالگان تاييد نشده

Ohio Library and Information Network.

تاريخ عمليات

20150814093936.6

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y