Geometric Integration Theory

by Hassler Whitney

Overview

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.

Product Details

ISBN-13:	9780691626703
Publisher:	Princeton University Press
Publication date:	12/08/2015
Series:	Princeton Legacy Library , #2210
Pages:	404
Product dimensions:	6.20(w) x 9.10(h) x 1.00(d)

Table of Contents

• 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