1 - Tensor Calculus

Abstract

The concepts of tensor analysis arose from the work of Carl Friedrich Gauss in differential geometry, and the formulation was much influenced by the theory of algebraic forms and invariants developed during the middle of the nineteenth century. The word “tensor” itself was introduced in 1846 by William Rowan Hamilton to describe something different from what is now meant by a tensor (Note 1) The contemporary usage was brought in by Voigt in 1898. Tensor calculus was developed around 1890 by Gregorio Ricci-Curbastro under the title absolute differential calculus, and originally presented by Ricci in 1892. It was made accessible to many mathematicians by the publication of Ricci and Tullio Levi-Civita's 1900 classic text Méthodes de calcul différentiel absolu et leurs applications (translated into Methods of absolute differential calculus and their applications).