A primer on exterior differential calculus

D.A. Burton
2003 Theoretical and Applied Mechanics  
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 R 3 is cast in terms of exterior calculus and the traditional Stokes' and
more » ... itional 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.
doi:10.2298/tam0302085b fatcat:tzxiubgrvfcs3lztdncowefhda