AngeloG said:
Nope.
Once you get into specific areas of Physics; each his it's own separate language to go with it essentially. Such as Calculus is really the "language" of classical/general physics. But later down the road you may use tensors, you may use different things. You really can't get this from Wikipedia.
I disagree. I first studied tensors years ago. Then couple of years later I studied tensors again and was confused at how different it was. I was never given an explanation of the reason for the difference, but accepted it nevertheless. Only last year did it all make sense to me, thanks to wikipedia:
"There are equivalent approaches to visualizing and working with tensors; that the content is actually the same may only become apparent with some familiarity with the material.
The classical approach
The classical approach views tensors as multidimensional arrays that are n-dimensional generalizations of scalars, 1-dimensional vectors and 2-dimensional matrices. The "components" of the tensor are the values in the array. This idea can then be further generalized to tensor fields, where the elements of the tensor are functions, or even differentials.
However, to count as a tensor, the arrays need to transform correctly when the reference co-ordinate system is changed. This transformation is a generalisation of the relationship which holds for vector components, and is similarly an expression of the independence of the underlying entity from the reference frame in which it is expressed.
The modern approach
The modern (component-free) approach views tensors initially as abstract objects, expressing some definite type of multi-linear concept. Their well-known properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of linear algebra to multilinear algebra. This treatment has attempted to replace the component-based treatment for advanced study, in the way that the more modern component-free treatment of vectors replaces the traditional component-based treatment after the component-based treatment has been used to provide an elementary motivation for the concept of a vector. You could say that the slogan is 'tensors are elements of some tensor space'. Nevertheless, a component-free approach has not become fully popular, owing to the difficulties involved with giving a geometrical interpretation to higher-rank tensors.
The intermediate treatment of tensors article attempts to bridge the two extremes, and to show their relationships.
In the end the same computational content is expressed, both ways. See glossary of tensor theory for a listing of technical terms."
