absolute differential calculus

English

Noun

absolute differential calculus (uncountable)

1. (mathematical analysis, dated or historical) Ricci calculus; the rules of index notation and manipulation for tensors and tensor fields, as developed by Gregorio Ricci-Curbastro.
   • 1926 [Blackie & Son], Marjorie Long (translator), Tullio Levi-Civita, The Absolute Differential Calculus (Calculus of Tensors), 1977, Dover [1].
   • 1931 [Blackie Company], A. J. McConnell, Applications of Tensor Analysis, 1957, Dover, page v,

     The absolute differential calculus came into prominence as the instrument best fitted for dealing with the general theory of relativity and it has also been found indispensable for the differential geometry of hyperspaces.

   • 1999, Umberto Bottazzini, “8: Ricci and Levi-Civita: from differential invariants to general relativity”, in Jeremy Gray, editor, The Symbolic Universe: Geometry and Physics 1890-1930, Oxford University Press, page 241:

     Instead, it is of interest to try to look at the emergence of the absolute differential calculus (ADC in the rest of this chapter) from the viewpoint of the mathematical community of the time.

Translations

Ricci calculus — see Ricci calculus

See also

• tensor analysis

Further reading

• Tensor calculus on Wikipedia.Wikipedia
• Tensor field on Wikipedia.Wikipedia
• Abstract index notation on Wikipedia.Wikipedia
• Mathematics of general relativity on Wikipedia.Wikipedia
• Tensor calculus on Encyclopedia of Mathematics