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Titlebook: Vector Analysis; Klaus Jänich Textbook 20011st edition Springer-Verlag New York 2001 Derivative.Vector field.calculus.differential equatio

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书目名称Vector Analysis
编辑Klaus Jänich
视频videohttp://file.papertrans.cn/981/980819/980819.mp4
丛书名称Undergraduate Texts in Mathematics
图书封面Titlebook: Vector Analysis;  Klaus Jänich Textbook 20011st edition Springer-Verlag New York 2001 Derivative.Vector field.calculus.differential equatio
描述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.
出版日期Textbook 20011st edition
关键词Derivative; Vector field; calculus; differential equation; differential geometry; manifold
版次1
doihttps://doi.org/10.1007/978-1-4757-3478-2
isbn_softcover978-1-4419-3144-3
isbn_ebook978-1-4757-3478-2Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightSpringer-Verlag New York 2001
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Undergraduate Texts in Mathematicshttp://image.papertrans.cn/v/image/980819.jpg
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Manifolds-with-Boundary,The classical version of Stokes’s theorem deals with the con­nection between “surface integrals” and “line integrals.” A three-dimensional version, called Gauss’s integral theorem, makes a statement about the relationship between “volume integrals” and surface integrals.
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,The Intuitive Meaning of Stokes’s Theorem,The actual definition of the Cartan (or exterior) derivative . : Ω.. → Ω.. will be postponed until the next chapter, and the proof of Stokes’s theorem that ... = ... until the chapter after that. In the present chapter I’ll try to sketch how one could intuitively come up with the idea of the exterior derivative and conjecture Stokes’s theorem.
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The Wedge Product and the Definition of the Cartan Derivative,To define the Cartan derivative we use a tool from multilinear algebra, the exterior, or “wedge,” product of alternating multilinear forms.
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