What is the meaning of tensor calculus?

[Vance Grey]

https://www.physicsforums.com/attachments/205736

 

[Vance Grey]

I need help.

 

[Greg Bernhardt]

Maybe you can start here
https://www.physicsforums.com/insights/what-is-a-tensor/

 

[fresh_42]

https://www.physicsforums.com/attachments/205736

Not sure, whether this is correct what I'm going to say, because "calculus" as an English word is often used quite synonymous to "analysis" whereas in my language it means "system of calculation methods". So I interpret it in the sense of the latter and understand "tensor calculus" as computational methods where tensors are used. This could simply be how to deal with tensors, or a rather algebraic point of view if we consider tensor algebras and their categorical properties, or a topological point of view if we consider tensor fields, which are similar defined as vector fields, or analytically - and this is more likely - the connection of tensors on one hand, and tangent spaces, curvatures and differential forms on the other hand. Personally I would all of them summarize under "tensor calculus" and only spent a different amount of space for the different perspectives.

 

[berkeman]

https://www.physicsforums.com/attachments/205736

Link is broken...

 

[WWGD]

Not sure, whether this is correct what I'm going to say, because "calculus" as an English word is often used quite synonymous to "analysis" whereas in my language it means "system of calculation methods". So I interpret it in the sense of the latter and understand "tensor calculus" as computational methods where tensors are used. This could simply be how to deal with tensors, or a rather algebraic point of view if we consider tensor algebras and their categorical properties, or a topological point of view if we consider tensor fields, which are similar defined as vector fields, or analytically - and this is more likely - the connection of tensors on one hand, and tangent spaces, curvatures and differential forms on the other hand. Personally I would all of them summarize under "tensor calculus" and only spent a different amount of space for the different perspectives.

Similar in English, actually, Calculus, sometimes 'Algebra' is used, as the rules used to operate with/on the objects.