Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Pugh, Charles Chapman (1940-....)
Pugh, Charles C.
Titre(s) : Real mathematical analysis [Texte électronique] / Charles Chapman Pugh
Édition : 2nd edition
Publication : Cham : Springer, 2015
Description matérielle : 1 ressource dématérialisée
Collection : Undergraduate texts in mathematics
Note(s) : Titre de l'écran-titre (visionné le 4 mars 2016). - Comprend des références bibliographiques
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
Sujet(s) : Analyse mathématique
Indice(s) Dewey :
515 (23e éd.) = Analyse (mathématiques) ; 515.42 (23e éd.) = Théorie de la mesure et théorie de l'intégration
Identifiants, prix et caractéristiques : ISBN 9783319177717
Identifiant de la notice : ark:/12148/cb446794959
Notice n° :
FRBNF44679495
(notice reprise d'un réservoir extérieur)
Table des matières : Real Numbers ; A Taste of Topology ; Functions of a Real Variable ; Function Spaces
; Multivariable Calculus ; Lebesgue Theory.
