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: Journal Article
Journal or Publication Title: Theoretical and Applied Mechanics
Subjects:
Departments: Faculty of Science and Technology > Physics
ID Code: 50495
Deposited By: ep_importer_pure
Deposited On: 27 Oct 2011 09:23
Refereed?: Yes
Published?: Published
Last Modified: 24 Jun 2019 00:24
URI: https://eprints.lancs.ac.uk/id/eprint/50495

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