Vector Analysis
By: by Klaus Jänich
Series: Undergraduate Texts in Mathematics; Undergraduate texts in mathematics
Publisher: Springer New York
Published: 2001
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 283
ISBN-13: 9781441931443; 9781475734782
Subjects: Mathematics; Cell aggregation
Description: 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.
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Mode of access: World Wide Web.
Table of contents: title: Differentiable manifolds; title: Tangent vector space; title: Differential forms; title: Orientability; title: Integration on manifolds; title: Open manifolds; title: The intuitive meaning of Stokes' theorem; title: The hat product and the definition of Cartan's derivative; title: Stokes' theorem; title: Classical vector analysis; title: De Rham cohomology; title: Differential forms on Riemannian manifolds; title: Calculating in coordinates; title: Answers; title: References; title: Index.