书目名称 | Vector Analysis | 编辑 | Klaus Jänich | 视频video | http://file.papertrans.cn/981/980819/980819.mp4 | 丛书名称 | Undergraduate Texts in Mathematics | 图书封面 |  | 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 | doi | https://doi.org/10.1007/978-1-4757-3478-2 | isbn_softcover | 978-1-4419-3144-3 | isbn_ebook | 978-1-4757-3478-2Series ISSN 0172-6056 Series E-ISSN 2197-5604 | issn_series | 0172-6056 | copyright | Springer-Verlag New York 2001 |
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