Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorJรคnich, Klaus. author
TitleVector Analysis [electronic resource] / by Klaus Jรคnich
ImprintNew York, NY : Springer New York : Imprint: Springer, 2001
Connect tohttp://dx.doi.org/10.1007/978-1-4757-3478-2
Descript XIV, 284 p. online resource

SUMMARY

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


CONTENT

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 Stokesโ{128}{153}s Theorem -- 8 The Wedge Product and the Definition of the Cartan Derivative -- 9 Stokesโ{128}{153}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


Mathematics Manifolds (Mathematics) Complex manifolds Mathematics Manifolds and Cell Complexes (incl. Diff.Topology)



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram