Derivation and Integration

A 2001 treatment of the classical problem of derivation and integration, with applications to the Gauss-Green and Stokes theorems.

Washek F. Pfeffer (Author)

9780521792684, Cambridge University Press

Hardback, published 5 March 2001

284 pages
22.9 x 15.2 x 1.9 cm, 0.59 kg

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

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.

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.

Subject Areas: Geometry [PBM], Calculus & mathematical analysis [PBK]