02246nmm a2200289 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001900139245006300158250001700221260004800238300003200286505048500318653002200803653002800825653005500853710003400908041001900942989003800961490003900999856007201038082001101110520083501121EB000631503EBX0100000000000000048458500000000000000.0cr|||||||||||||||||||||140122 ||| eng a97814757347821 aJänich, Klaus00aVector AnalysishElektronische Ressourcecby Klaus Jänich a1st ed. 2001 aNew York, NYbSpringer New Yorkc2001, 2001 aXIV, 284 pbonline resource0 a1 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 aComplex manifolds aManifolds (Mathematics) aManifolds and Cell Complexes (incl. Diff.Topology)2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aUndergraduate Texts in Mathematics uhttps://doi.org/10.1007/978-1-4757-3478-2?nosfx=yxVerlag3Volltext0 a514.34 aClassical 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