000			03994cam a2200397Mi 4500
003			OCoLC
005			20220330120708.0
006			m o d
007			cr |n|||||||||
008			140314s2014 enk ob 001 0 eng d
020			_z9780123944030 _q(alk. paper)
035			_aGSU00364 _z(OCoLC)871224203 _z(OCoLC)875004005
040			_aLCC _benglish _cGSU _dGSU _erda
050		4	_aQA381 _bWEI
082	0	4	_a515/.37 _223 _bWEI
090			_aONLINE
100	1		_aWeintraub, Steven H., _eauthor.
245	1	0	_aDifferential forms : _btheory and practice / _cby Steve Weintraub.
250			_aSecond edition.
264		1	_aOxford, UK : _bElsevier, _c2014.
300			_axi;395pages;
336			_atext _btxt _2rdacontent.
337			_acomputer _bc _2rdamedia.
338			_aonline resource _bcr _2rdacarrier.
504			_aIncludes bibliographical references and index.
505	0		_aHalf Title; Title Page; Copyright; Dedication; Contents; Preface; 1 Differential Forms in Rn, I; 1.0 Euclidean spaces, tangent spaces, and tangent vector fields; 1.1 The algebra of differential forms; 1.2 Exterior differentiation; 1.3 The fundamental correspondence; 1.4 The Converse of Poincaré's Lemma, I; 1.5 Exercises; 2 Differential Forms in Rn, II; 2.1 1-Forms; 2.2 k-Forms; 2.3 Orientation and signed volume; 2.4 The converse of Poincaré's Lemma, II; 2.5 Exercises; 3 Push-forwards and Pull-backs in Rn; 3.1 Tangent vectors; 3.2 Points, tangent vectors, and push-forwards.
505	8		_a3.3 Differential forms and pull-backs3.4 Pull-backs, products, and exterior derivatives; 3.5 Smooth homotopies and the Converse of Poincaré's Lemma, III; 3.6 Exercises; 4 Smooth Manifolds; 4.1 The notion of a smooth manifold; 4.2 Tangent vectors and differential forms; 4.3 Further constructions; 4.4 Orientations of manifolds'227intuitive discussion; 4.5 Orientations of manifolds'227careful development; 4.6 Partitions of unity; 4.7 Smooth homotopies and the Converse of Poincaré's Lemma in general; 4.8 Exercises; 5 Vector Bundles and the Global Point of View.
505	8		_a5.1 The definition of a vector bundle5.2 The dual bundle, and related bundles; 5.3 The tangent bundle of a smooth manifold, and related bundles; 5.4 Exercises; 6 Integration of Differential Forms; 6.1 Definite integrals in textmathbbRn; 6.2 Definition of the integral in general; 6.3 The integral of a 0-form over a point; 6.4 The integral of a 1-form over a curve; 6.5 The integral of a 2-form over a surface; 6.6 The integral of a 3-form over a solid body; 6.7 Chains and integration on chains; 6.8 Exercises; 7 The Generalized Stokes's Theorem; 7.1 Statement of the theorem.
505	8		_a7.2 The fundamental theorem of calculus and its analog for line integrals7.3 Cap independence; 7.4 Green's and Stokes's theorems; 7.5 Gauss's theorem; 7.6 Proof of the GST; 7.7 The converse of the GST; 7.8 Exercises; 8 de Rham Cohomology; 8.1 Linear and homological algebra constructions; 8.2 Definition and basic properties; 8.3 Computations of cohomology groups; 8.4 Cohomology with compact supports; 8.5 Exercises; Index; A; B; C; D; E; F; G; H; I; L; M; N; O; P; R; S; T; V; W.
520			_aDifferential forms are utilized as a mathematical technique to help students, researchers, and engineers analyze and interpret problems where abstract spaces and structures are concerned, and when questions of shape, size, and relative positions are involved. Differential Forms has gained high recognition in the mathematical and scientific community as a powerful computational tool in solving research problems and simplifying very abstract problems through mathematical analysis on a computer. Differential Forms, 2nd Edition, is a solid resource for students and prof.
588			_aPrint version record.
650		0	_aDifferential forms.
655		0	_aElectronic books. _0http://id.loc.gov/authorities/subjects/sh93007047.
776	0	8	_iPrint version: _z9780123944030 _z0123944031 _w(DLC) 2013035820.
942			_2lcc _cBK _n0
999			_c420 _d420