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A primer on exterior differential calculus

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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A primer on exterior differential calculus. / Burton, David A.
In: Theoretical and Applied Mechanics, Vol. 30, 2003, p. 85-162.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Burton, DA 2003, 'A primer on exterior differential calculus', Theoretical and Applied Mechanics, vol. 30, pp. 85-162. https://doi.org/10.2298/TAM0302085B

APA

Burton, D. A. (2003). A primer on exterior differential calculus. Theoretical and Applied Mechanics, 30, 85-162. https://doi.org/10.2298/TAM0302085B

Vancouver

Burton DA. A primer on exterior differential calculus. Theoretical and Applied Mechanics. 2003;30:85-162. doi: 10.2298/TAM0302085B

Author

Burton, David A. / A primer on exterior differential calculus. In: Theoretical and Applied Mechanics. 2003 ; Vol. 30. pp. 85-162.

Bibtex

@article{da697b134bd74ede8ec2be165f84d171,
title = "A primer on exterior differential calculus",
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.",
keywords = "manifolds, differential geometry , exterior calculus , differential forms , tensor calculus , linear connections",
author = "Burton, {David A}",
year = "2003",
doi = "10.2298/TAM0302085B",
language = "English",
volume = "30",
pages = "85--162",
journal = "Theoretical and Applied Mechanics",
publisher = "Serbian Society for Mechanics",

}

RIS

TY - JOUR

T1 - A primer on exterior differential calculus

AU - Burton, David A

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - manifolds

KW - differential geometry

KW - exterior calculus

KW - differential forms

KW - tensor calculus

KW - linear connections

U2 - 10.2298/TAM0302085B

DO - 10.2298/TAM0302085B

M3 - Journal article

VL - 30

SP - 85

EP - 162

JO - Theoretical and Applied Mechanics

JF - Theoretical and Applied Mechanics

ER -