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Tensor calculus

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Title: Tensor calculus  
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Subject: Calculus, Palatini identity, Tensors in curvilinear coordinates, Ricci calculus, Mean value theorem
Collection: Calculus, Tensors
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Tensor calculus

In mathematics, tensor calculus or tensor analysis is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).

Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his theory of general relativity. Contrasted with the infinitesimal calculus, tensor calculus allows presentation of physics equations in a form that is independent of the choice of coordinates on the manifold.

Tensor calculus has many real-life applications in physics and engineering, including stress analysis, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), and general relativity (see mathematics of general relativity).

See also

Books

  • Dimitrienko, Yuriy (2002). Tensor Analysis and Nonlinear Tensor Functions. Kluwer Academic Publishers (Springer).  
  • J.R. Tyldesley (1973). An introduction to Tensor Analysis: For Engineers and Applied Scientists. Longman.  
  • D.C. Kay (1988). Tensor Calculus. Schaum’s Outlines, McGraw Hill (USA).  



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