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This 2001 treatment of the classical problem of derivation and integration combines the techniques of analysis with those of geometric measure theory. The main applications are to the Gauss-Green and Stokes theorems. The many results are proved in detail, and include background material and precise references to well-known results.

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.

Boekdetails

Serie
Cambridge Tracts in Mathematics
Ondertitel
Cambridge Tracts in Mathematics
Formaat
Digital download and online
Uitgever
Cambridge University Press
Imprint
Cambridge University Press (Virtual Publishing)
Auteur
Washek F. Pfeffer (University of California, Davis), Cambridge University Press (Virtual Publishing), Cambridge University Press
ISBN-13
9780511574764
Verschijningsdatum
2014-07-05
Land van herkomst
GB

Digital download and online

Derivation and Integration

door Washek F. Pfeffer (University of California, Davis)

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