Abstract

A primer on exterior differential calculus D.A. Burton∗ Theoret. Appl. Mech., Vol. 30, No. 2, pp. 85-162, Belgrade 2003 A pedagogical application-oriented introduction to the cal-culus of exterior differential forms on differential manifolds is presented. Stokes ’ theorem, the Lie derivative, linear con-nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi-tional 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 exte-rior expression of Stokes ’ theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The nu-merous advantages of this calculus, over more traditional ma-chinery, are stressed throughout the article