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Beschreibung
A working knowledge of differential forms so strongly illuminates the calculus and its developments that it ought not be too long delayed in the curriculum. On the other hand, the systematic treatment of differential forms requires an apparatus of topology and algebra which is heavy for beginning undergraduates. Several texts on advanced calculus using differential forms have appeared in recent… years. We may cite as representative of the variety of approaches the books of Fleming [2], (1) Nickerson-Spencer-Steenrod [3], and Spivak [6]. . Despite their accommodation to the innocence of their readers, these texts cannot lighten the burden of apparatus exactly because they offer a more or less full measure of the truth at some level of generality in a formally precise exposition. There. is consequently a gap between texts of this type and the traditional advanced calculus. Recently, on the occasion of offering a beginning course of advanced calculus, we undertook the expe- ment of attempting to present the technique of differential forms with minimal apparatus and very few prerequisites. These notes are the result of that experiment. Our exposition is intended to be heuristic and concrete. Roughly speaking, we take a differential form to be a multi-dimensional integrand, such a thing being subject to rules making change-of-variable calculations automatic. The domains of integration (manifolds) are explicitly given "surfaces" in Euclidean space. The differentiation of forms (exterior (1) Numbers in brackets refer to the Bibliography at the end. 53,49 €
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Technische Daten
Erscheinungsdatum
11.06.1984
Sprache
Englisch
EAN
9780387902876
Herausgeber
Springer US
Serien- oder Bandtitel
Universitext
Sonderedition
Nein
Autor
M. Schreiber
Seitenanzahl
150
Einbandart
Broschiert
Buch Untertitel
A Heuristic Introduction
Schlagwörter
Differentialform, exterior derivative, integration, manifold
Thema-Inhalt
PBMP - Differentielle und Riemannsche Geometrie
Höhe
244 mm
Breite
17 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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