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＜電子ブック＞
Vector Analysis / by Klaus Jänich
(Undergraduate Texts in Mathematics. ISSN:21975604)

版	1st ed. 2001.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2001
本文言語	英語
大きさ	XIV, 284 p : online resource
著者標目	*Jänich, Klaus author SpringerLink (Online service)
件　名	LCSH:Manifolds (Mathematics) FREE:Manifolds and Cell Complexes
一般注記	1 Differentiable Manifolds -- 2 The Tangent Space -- 3 Differential Forms -- 4 The Concept of Orientation -- 5 Integration on Manifolds -- 6 Manifolds-with-Boundary -- 7 The Intuitive Meaning of Stokes’s Theorem -- 8 The Wedge Product and the Definition of the Cartan Derivative -- 9 Stokes’s Theorem -- 10 Classical Vector Analysis -- 11 De Rham Cohomology -- 12 Differential Forms on Riemannian Manifolds -- 13 Calculations in Coordinates -- 14 Answers to the Test Questions Classical vector analysis deals with vector fields; the gradient, divergence, and curl operators; line, surface, and volume integrals; and the integral theorems of Gauss, Stokes, and Green. Modern vector analysis distills these into the Cartan calculus and a general form of Stokes' theorem. This essentially modern text carefully develops vector analysis on manifolds and reinterprets it from the classical viewpoint (and with the classical notation) for three-dimensional Euclidean space, then goes on to introduce de Rham cohomology and Hodge theory. The material is accessible to an undergraduate student with calculus, linear algebra, and some topology as prerequisites. The many figures, exercises with detailed hints, and tests with answers make this book particularly suitable for anyone studying the subject independently HTTP:URL=https://doi.org/10.1007/978-1-4757-3478-2

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