Description
Book SynopsisA 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
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
