11 Historical Overview of Development Use of Tensor Calculus First we should

# 11 historical overview of development use of tensor

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1.1 Historical Overview of Development & Use of Tensor Calculus First, we should remark that some of the following historical statements represent approx- imate rather than exact historical facts due to the reality that many of the first hand historical records are missing or not available to the author. Moreover, many ideas, termi- nology, notation and techniques of tensor calculus, like any other field of knowledge and practice, have been developed gradually over long periods of time although the credit is usually attributed to a few individuals due to their prominence and fame or because they played crucial and distinctive roles in the creation and development of the subject. It is believed that the word “ tensor ” was coined by Hamilton but he used it in a rather different meaning to what is being used for in modern mathematics and science. 8
1.1 Historical Overview of Development & Use of Tensor Calculus 9 The credit for attaching this term to its modern technical meaning, approximately in the late nineteenth century, is usually given to Voigt . Apparently, the term “ tensor was originally derived from the Latin word “ tensus ” which means tension or stress since one of the first uses of tensors (in whatever meaning) was related to the mathematical description of mechanical stress. The names “ tensor calculus ” or “ tensor analysis ” have been used to label this sub- ject in its modern form rather recently, probably in the second quarter of the twenties century. The early forms of this subject have been called “ Ricci calculus ” or “ absolute differential calculus ”. The latter names may still be found in the modern literature of tensor calculus. Many mathematicians and scientists have contributed to the development of tensor cal- culus directly or indirectly. However, numerous components of the modern tensor calculus were not developed as such and for the purpose of the theory of tensors but as parts or byproducts of other disciplines, notably the differential geometry of curves and surfaces. This generally applies prior to the official launch of tensor calculus as an independent branch of mathematics by Ricci and Levi-Civita who are commonly recognized as the founding fathers of this discipline. Several concepts and techniques of tensor calculus have been developed by Gauss and Riemann in the nineteenth century, mainly as part of their efforts to develop and for- mulate the theory of differential geometry of curves and surfaces. Their contributions are highlighted by the fact that many concepts, methods and equations, which are related directly to tensor calculus or to subjects with a close affinity to tensor calculus, bear their names, e.g. Gaussian coordinates, Gauss curvature tensor, Gauss-Codazzi equations, Rie- mannian metric tensor, Riemannian manifold, and Riemann-Christoffel curvature tensor.

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• Summer '20
• Rajendra Paramanik
• Tensor, Coordinate system, Polar coordinate system, Coordinate systems

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