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008			120720s2012 flu sb 001 0 eng d
020			_a9781466507210 (ebook : PDF)
040			_aFlBoTFG _cFlBoTFG
090			_aQA433 _b.P493 2012
092			_a515.4 _bP524
100	1		_aPfeffer, Washek F.
245	1	4	_aThe divergence theorem and sets of finite perimeter _h[electronic resource] / _cWashek F. Pfeffer.
260			_aBoca Raton : _bCRC Press, _c2012.
300			_axv, 242 p.
490	1		_aMonographs and textbooks in pure and applied mathematics
500			_a"A Chapman & Hall book."
504			_aIncludes bibliographical references (p. 231-233) and index.
505	0		_apt. 1. Dyadic figures -- pt. 2. Sets of finite perimeter -- pt. 3. The divergence theorem.
520			_a"Preface The divergence theorem and the resulting integration by parts formula belong to the most frequently used tools of mathematical analysis. In its elementary form, that is for smooth vector fields defined in a neighborhood of some simple geometric object such as rectangle, cylinder, ball, etc., the divergence theorem is presented in many calculus books. Its proof is obtained by a simple application of the one-dimensional fundamental theorem of calculus and iterated Riemann integration. Appreciable difficulties arise when we consider a more general situation. Employing the Lebesgue integral is essential, but it is only the first step in a long struggle. We divide the problem into three parts. (1) Extending the family of vector fields for which the divergence theorem holds on simple sets. (2) Extending the the family of sets for which the divergence theorem holds for Lipschitz vector fields. (3) Proving the divergence theorem when the vector fields and sets are extended simultaneously. Of these problems, part (2) is unquestionably the most complicated. While many mathematicians contributed to it, the Italian school represented by Caccioppoli, De Giorgi, and others, obtained a complete solution by defining the sets of bounded variation (BV sets). A major contribution to part (3) is due to Federer, who proved the divergence theorem for BV sets and Lipschitz vector fields. While parts (1)-(3) can be combined, treating them separately illuminates the exposition. We begin with sets that are locally simple: finite unions of dyadic cubes, called dyadic figures. Combining ideas of Henstock and McShane with a combinatorial argument of Jurkat, we establish the divergence theorem for very general vector fields defined on dyadic figures"-- _cProvided by publisher.
530			_aAlso available in print edition.
538			_aMode of access: World Wide Web.
650		0	_aDivergence theorem.
650		0	_aDifferential calculus.
655		7	_aElectronic books. _2lcsh
776	1		_z9781466507197 (hardback)
830		0	_aMonographs and textbooks in pure and applied mathematics.
856	4	0	_uhttp://marc.crcnetbase.com/isbn/9781466507210 _qapplication/PDF _zDistributed by publisher. Purchase or institutional license may be required for access.
999			_c15290 _d15290