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题名/责任者:

Differential forms : theory and practice = 微分形式 : 理论与练习 / [美] Weintraub, S. H.(温特劳斯)著.

版本说明:

第1版.

出版发行项:

哈尔滨 : Harbin Institute of Technology Press, 2015.

ISBN:

9787560355184

载体形态项:

v, 395 pages : illustrations ; 25 cm.

变异题名:

微分形式 : 理论与练习

丛编说明:

国外优秀数学著作原版系列

个人责任者:

Weintraub, Steven H., author.

论题主题:

Differential forms.

中图法分类号:

O186.15

一般附注:

Includes index.

内容附注:

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 Poincares Lemma, I -- 1.5.Exercises -- 2.1.1-Forms -- 2.2.k-Forms -- 2.3.Orientation and signed volume -- 2.4.The Converse of Poincarés Lemma, II -- 2.5.Exercises -- 3.1.Tangent vectors -- 3.2.Points, tangent vectors, and push-forwards -- 3.3.Differential forms and pull-backs -- 3.4.Pull-backs, products, and exterior derivatives -- 3.5.Smooth homotopies and the Converse of Poincarés Lemma, III -- 3.6.Exercises -- 4.1.The notion of a smooth manifold -- 4.2.Tangent vectors and differential forms -- 4.3.Further constructions -- 4.4.Orientations of manifolds-intuitive discussion -- 4.5.Orientations of manifolds-careful development -- 4.6.Partitions of unity -- 4.7.Smooth homotopies and the Converse of Poincares Lemma in general -- 4.8.Exercises --

内容附注:

Contents note continued: 5.1.The definition of a vector bundle -- 5.2.The dual bundle, and related bundles -- 5.3.The tangent bundle of a smooth manifold, and related bundles -- 5.4.Exercises -- 6.1.Definite integrals in Rn -- 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 -- 7.1.Statement of the theorem -- 7.2.The fundamental theorem of calculus and its analog for line integrals -- 7.3.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 -- 8.1.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.

原版附注:

Reprint. Originally published: Boston : Elsevier, c2014. 2nd ed. 9780123944030.

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