Real Mathematical Analysis | Taschenbuch

Cover: 9783319330426 | Real Mathematical Analysis | Charles Chapman Pugh | Taschenbuch | xi

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Charles C. Pugh is Professor Emeritus at the University of California, Berkeley. His research interests include geometry and topology, dynamical systems, and normal hyperbolicity.

Zusammenfassung

Elucidates abstract concepts and salient points in proofs with over 150 detailed illustrations

Treats the rigorous foundations of both single and multivariable Calculus

Gives an intuitive presentation of Lebesgue integration using the undergraph approach of Burkill

Includes over 500 exercises that are interesting and thought-provoking, not merely routine

Inhaltsverzeichnis

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

Details

Erscheinungsjahr:	2016
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xi 478 S. 1 farbige Illustr. 478 p. 1 illus. in color.
ISBN-13:	9783319330426
ISBN-10:	331933042X
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Pugh, Charles Chapman
Auflage:	Softcover reprint of the original 2nd ed. 2015
Hersteller:	Springer International Publishing Springer International Publishing AG Undergraduate Texts in Mathematics
Maße:	254 x 178 x 27 mm
Von/Mit:	Charles Chapman Pugh
Erscheinungsdatum:	15.10.2016
Gewicht:	0,916 kg

Artikel-ID: 102727558