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A primer on exterior differential calculus

Burton, David A (2003) A primer on exterior differential calculus. Theoretical and Applied Mechanics, 30. pp. 85-162.

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    Abstract

    A pedagogical application-oriented introduction to the cal­culus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear con­nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi­tional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The numerous advantages of this calculus, over more traditional ma­chinery, are stressed throughout the article.

    Item Type: Article
    Journal or Publication Title: Theoretical and Applied Mechanics
    Uncontrolled Keywords: manifolds ; differential geometry ; exterior calculus ; differential forms ; tensor calculus ; linear connections
    Subjects:
    Departments: Faculty of Science and Technology > Physics
    ID Code: 50495
    Deposited By: ep_importer_pure
    Deposited On: 27 Oct 2011 10:23
    Refereed?: Yes
    Published?: Published
    Last Modified: 08 Sep 2017 00:22
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/50495

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