Geometric Integration Theory

Hassler Whitney

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English

Princeton University Press
08 December 2015

Analytic geometry

Series: Princeton Legacy Library

A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

By: Hassler Whitney
Imprint: Princeton University Press
Country of Publication: United States
Volume: 3986
Dimensions: Height: 235mm, Width: 152mm, Spine: 21mm
Weight: 539g
ISBN: 9780691626703
ISBN 10: 0691626707
Series: Princeton Legacy Library
Pages: 404
Publication Date: 08 December 2015
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

*Frontmatter, pg. i*Preface, pg. v*Table of Contents, pg. ix*Introduction, pg. 1*A. The general problem of integration, pg. 1*B. Some classical topics, pg. 13*C. Indications of general theory, pg. 27*Chapter I. Grassmann algebra, pg. 35*Chapter II. Differential forms, pg. 58*Chapter III. Riemann integration theory, pg. 79*Chapter IV. Smooth manifolds, pg. 112*Chapter V. Abstract integration theory, pg. 151*Chapter VI. Some relations between chains and functions, pg. 186*Chapter VII. General properties of chains and cochains, pg. 207*Chapter VIII. Chains and cochains in open sets, pg. 231*Chapter IX. Flat cochains and differential forms, pg. 253*Chapter X. Lipschitz mappings, pg. 288*Chapter XI. Chains and additive set functions, pg. 310*Appendix I. Vector and linear spaces, pg. 341*Appendix II. Geometric and topological preliminaries, pg. 355*Appendix III. Analytical preliminaries, pg. 371*Index of symbols, pg. 379*Index of terms, pg. 383