04608cam a2200517Mi 4500 ocn873760139 OCoLC 20190328114807.0 m o d cr |n||||||||| 140314s2014 enk ob 001 0 eng d YDXCP eng pn YDXCP OPELS UMI N$T COO CHVBK DEBBG OCLCQ OCLCF EBLCP DEBSZ OCLCQ OCLCO U3W D6H CEF OTZ 871224203 875004005 0123946174 (electronic bk.) 9780123946171 (electronic bk.) 9780123944030 (alk. paper) 0123944031 (alk. paper) (OCoLC)873760139 (OCoLC)871224203 (OCoLC)875004005 QA381 .W45 2014 MAT 005000 bisacsh MAT 034000 bisacsh 515/.37 23 Weintraub, Steven H., author. Differential forms : theory and practice / [electronic resource] by Steve Weintraub. 2nd ed. Oxford, UK : Elsevier, 2014. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references and index. Print version record. Half 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 Poincar�e'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 Poincar�e'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. 3.3 Differential forms and pull-backs3.4 Pull-backs, products, and exterior derivatives; 3.5 Smooth homotopies and the Converse of Poincar�e'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 Poincar�e's Lemma in general; 4.8 Exercises; 5 Vector Bundles and the Global Point of View. 5.1 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. 7.2 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. Differential 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. Differential forms. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Differential forms. fast (OCoLC)fst00893491 Differentialform gnd (DE-588)4149772-7 Electronic books. Print version: 9780123944030 0123944031 (DLC) 2013035820 ScienceDirect http://www.sciencedirect.com/science/book/9780123944030 246890 246890