Derivation and Integration

by Washek F. Pfeffer

Overview

This book, devoted to an invariant multidimensional process of recovering a function from its derivative, considers additive functions defined on the family of all bounded BV sets that are continuous with respect to a suitable topology. The main applications are related to the Gauss-Green and Stokes theorems. The book contains complete and detailed proofs of all new results, and of many known results for which the references are not easily available. It will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas.

Product Details

ISBN-13:	9780521792684
Publisher:	Cambridge University Press
Publication date:	03/05/2001
Series:	Cambridge Tracts in Mathematics , #140
Pages:	284
Product dimensions:	5.98(w) x 9.02(h) x 0.75(d)

Table of Contents

Preface; Acknowledgments; 1. Preliminaries; 2. Charges; 3. Variations of charges; 4. Charges and BV functions; 5. Integration; 6. Extending the integral; Bibliography; List of symbols; Index.

Editorial Reviews

Review of the hardback: '…warmly recommended to researchers and advanced graduate students …'. József Németh, Acta Sci. Math.

Review of the hardback: '…I warmly recommended this book …'. Thierry de Pauw, Bulletin of the Belgian Mathematical Society

Review of the hardback: ' … written by one of the leading specialists in this field.' EMS

Review of the hardback: 'Readers with a good background in analysis will find this an illuminating account.' Mathematika

From the Publisher

Pfeffer (emeritus, mathematics, U. of California, Davis) dissects a multidimensional version of the classical problem of recovering a function from its derivative. He considers additive functions defined on the family of all bounded BV sets that are continuous with respect to a suitable topology. A typical example is the flux of a continuous vector field. A general Gauss-Green theorem follows from the conditions sufficient for the derivability of the flux. Since the setting is invariant with respect to local lipeomorphisms, a standard argument extends the Gauss-Green theorem to the Stokes theorem on Lipschitz manifolds. The author also proves the Stokes theorem for a class of top-dimensional normal currents. Annotation c. Book News, Inc., Portland, OR (booknews.com)