Derivation and Integration

Washek F. Pfeffer

ISBN 10: 0521155657 / ISBN 13: 9780521155656

Published by Cambridge University Press, GB, 2010

About this Item

This 2001 book is devoted to an invariant multidimensional process of recovering a function from its derivative. It 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 very general Gauss-Green theorem follows from the sufficient conditions 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. In addition, the author proves the Stokes theorem for a class of top-dimensional normal currents - a first step towards solving a difficult open problem of derivation and integration in middle dimensions. The book contains complete and detailed proofs and will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas.

Seller Inventory # LU-9780521155656

Bibliographic Details

• Title: Derivation and Integration
• Publisher: Cambridge University Press, GB
• Publication Date: 2010
• Language: English
• ISBN 10: 0521155657
• ISBN 13: 9780521155656
• Binding: Paperback
• Condition: New
• Weight: 420 grams

About this title

Synopsis

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.

Book Description

Within the context of BV sets and functions, this book studies an invariant multidimensional process of recoevring a function from its derivative. The results are applied to the Gauss-Green and Stokes theorems. The author presents many new results, which are proved in detail, and includes background material and precise references to well-known results, making the treatment accessible to graduate students and researchers in functional analysis and geometric measure theory.