Differential forms : theory put into practice / by Steve Weintraub
 Publication:
 Oxford, [England] ; Amsterdam, The Netherlands : Academic Press, 2014
 Format/Description:
 Book
1 online resource (409 p.)  Edition:
 2nd ed.
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Details
 Subjects:
 Differential forms.
 Form/Genre:
 Electronic books.
 Language:
 English
 System Details:
 text file
 Summary:
 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
 Contents:
 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 Poincaré's Lemma, I; 1.5 Exercises; 2 Differential Forms in Rn, II; 2.1 1Forms; 2.2 kForms; 2.3 Orientation and signed volume; 2.4 The converse of Poincaré's Lemma, II; 2.5 Exercises; 3 Pushforwards and Pullbacks in Rn; 3.1 Tangent vectors; 3.2 Points, tangent vectors, and pushforwards
3.3 Differential forms and pullbacks3.4 Pullbacks, 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
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 0form over a point; 6.4 The integral of a 1form over a curve; 6.5 The integral of a 2form over a surface; 6.6 The integral of a 3form 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  Notes:
 Description based upon print version of record
Includes bibliographical references and index
Description based on print version record  ISBN:
 0123946174