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Tensor calculus has many applications in physics, engineering and computer science including elasticity, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory, and machine learning.
Gregorio Ricci-Curbastro (Italian: [ɡreˈɡɔːrjo ˈrittʃi kurˈbastro]; 12 January 1853 – 6 August 1925) was an Italian mathematician. [1] He is most famous as the discoverer of tensor calculus .
In the 1950s Schouten completely rewrote and updated the German version of Ricci-Kalkül and this was translated into English as Ricci Calculus. This covers everything that Schouten considered of value in tensor analysis. This included work on Lie groups and other topics and that had been much developed since the first edition.
Tullio Levi-Civita, ForMemRS [1] (English: / ˈ t ʊ l i oʊ ˈ l ɛ v i ˈ tʃ ɪ v ɪ t ə /, Italian: [ˈtulljo ˈlɛːvi ˈtʃiːvita]; 29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity, but who also made significant contributions in other areas.
Tensor calculus was developed around 1890 by Gregorio Ricci-Curbastro under the title absolute differential calculus, and originally presented in 1892. [18] It was made accessible to many mathematicians by the publication of Ricci-Curbastro and Tullio Levi-Civita 's 1900 classic text Méthodes de calcul différentiel absolu et leurs ...
In general relativity and tensor calculus, the contracted Bianchi identities are: [1] = where is the Ricci tensor, the scalar curvature, and indicates covariant differentiation.
Broadly, one could analogize the role of the Ricci curvature in Riemannian geometry to that of the Laplacian in the analysis of functions; in this analogy, the Riemann curvature tensor, of which the Ricci curvature is a natural by-product, would correspond to the full matrix of second derivatives of a function.
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.