High School Tensor Calculus vs Tensor Analysis?

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Tensor calculus and tensor analysis are often used interchangeably, but they have historical distinctions. Tensor calculus, developed by Gregorio Ricci-Curbastro in the late 19th century, focuses on the computational aspects of tensors, while tensor analysis encompasses broader theoretical frameworks. The term "tensor" was introduced in the mid-19th century, evolving significantly through contributions from mathematicians like Woldemar Voigt and later gaining prominence with Einstein's general relativity. The discussion highlights a common preference for the term "analysis" over "calculus" due to linguistic connotations. Overall, while the terms may overlap in modern usage, their origins reflect different emphases in the study of tensors.
ibkev
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I've seen the terms tensor calculus and tensor analysis both being used - what is the difference?
 
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As far as I know they are the same thing.

This wiki article backs that up in the History secton at the end of the article:

https://en.wikipedia.org/wiki/Tensor

...
History
The concepts of later 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.[18]The word "tensor" itself was introduced in 1846 by William Rowan Hamilton[19] to describe something different from what is now meant by a tensor.[Note 3] The contemporary usage was introduced by Woldemar Voigt in 1898.[20]

Tensor calculus was developed around 1890 by Gregorio Ricci-Curbastro under the title absolute differential calculus, and originally presented by Ricci in 1892.[21] 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 (Methods of absolute differential calculus and their applications).[22]

In the 20th century, the subject came to be known as tensor analysis, and achieved broader acceptance with the introduction ofEinstein's theory of general relativity, around 1915. General relativity is formulated completely in the language of tensors. Einstein had learned about them, with great difficulty, from the geometer Marcel Grossmann.[23] Levi-Civita then initiated a correspondence with Einstein to correct mistakes Einstein had made in his use of tensor analysis. The correspondence lasted 1915–17, and was characterized by mutual respect:
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I assume it's the same as between calculus and analysis. I've said analysis my whole life and only use calculus in the English language.
It simply sounds far too much like calculator.
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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