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 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 ma?chinery, are stressed throughout the article. .Ovaj uvod u spoljasnje diferencijalne forme na diferencijalnim mnogostrukostima je orijentisan, pre svega, na pedagoski pristup i primenu na konkretne probleme. Teorema Stokes-a, Lie-ov izvod, linearne koneksije sa njihovom krivinom, torzijom i nemetricnoscu se diskutuju. Dati su brojni primeri uradjeni ovom metodom i detaljna uporedjenja sa odgovarajucim tradicionalnim vektorskim metodom cine znacajan deo ovog rada. Posebno vektorski racun na R3 je izrazen pomocu spoljasnjeg racuna te se tako tradicionalne teoreme Stokes-a i divergencije zamenjuju snaznijim spoljasnjim izrazom teoreme Stokes-a.Primeri iz klasicne mehanike kontinuuma kao i fizike prostor-vremena se diskutuju i izvode jezikom spoljasnjih diferencijalnih formi. Brojne prednosti ovog racuna u odnosu na tradicionalnu "masineriju" su nagla?sene tokom citavog izlaganja. .
CITATION STYLE
Burton, D. A. (2003). A primer on exterior differential calculus. Theoretical and Applied Mechanics, (30), 85–162. https://doi.org/10.2298/tam0302085b
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