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Universitext

Differential Forms

A Heuristic Introduction

Authors: Schreiber, M.

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About this Textbook

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.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-1-4612-9940-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.99
price for USA in USD
  • ISBN 978-0-387-90287-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Differential Forms
Book Subtitle
A Heuristic Introduction
Authors
Series Title
Universitext
Copyright
1977
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag, New York Inc.
eBook ISBN
978-1-4612-9940-0
DOI
10.1007/978-1-4612-9940-0
Softcover ISBN
978-0-387-90287-6
Series ISSN
0172-5939
Edition Number
1
Number of Pages
X, 150
Topics