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ISBN: 0521792681 9780521792684 9780511574764 9780521155656 Year: 2001 Volume: 140 Publisher: Cambridge Cambridge University Press
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ISBN: 0511574762 Year: 2001 Publisher: Cambridge : Cambridge University Press,
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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.
ISBN: 1281956317 9786611956318 981281065X 9789812810656 9781281956316 9789810242398 9810242395 Year: 2001 Publisher: Singapore River Edge, NJ World Scientific
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A presentation of the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. A basic knowledge of introductory real analysis is required of the reader.
Henstock-Kurzweil integral. --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Gauge integral --- Generalized Riemann integral --- Henstock integrals --- HK integral --- Kurzweil-Henstock integral --- Kurzweil integral --- Riemann integral, Generalized --- Integrals, Generalized
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