E-Book, Englisch, 404 Seiten
Reihe: Princeton Legacy Library
Whitney Geometric Integration Theory
Erscheinungsjahr 2016
ISBN: 978-1-4008-7757-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 404 Seiten
Reihe: Princeton Legacy Library
ISBN: 978-1-4008-7757-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
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
