====== Tensor Calculus ======


<tabbox Intuitive> 

<blockquote>A tensor is a relation between one vector and another. If you start with one vector, such as a force, and mathematically apply it to a tensor, then you get another vector. That vector might be, for example, the stress caused by the force.

That’s the simplest thing they do. Tensors do other things too; for example, the metric tensor represent the geometry of space. A tensor can represent the energy-momentum density. A tensor can represent a combination of electric and magnetic fields in a way that some of Maxwell’s equations greatly simplify. But the simplest and most basic connection is the vector to vector one.

A function relates one number (a “scalar”) to another one. A tensor does that for vectors.<cite>http://qr.ae/TUTNzc</cite></blockquote>
  
<tabbox Concrete> 
**Recommended Books**



  * [[http://amzn.to/2zqbkeU|A Student's Guide to Vectors and Tensors]] by Fleisch - a nice student-friendly introduction
  * [[http://maths.dur.ac.uk/users/kasper.peeters/pdf/tensor_en.pdf|Introduction to Tensor Calculus]] by Kees Dullemond & Kasper Peeters (free)
  * A Brief on Tensor Analysis by James Simmonds - a concise but great introductory text.
<tabbox Abstract> 

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

<tabbox Why is it interesting?> 

<blockquote>Tensor calculus is a technique that can be regarded as a follow-up on linear algebra.
It is a generalization of classical linear algebra. In classical linear algebra one deals
with vectors and matrices. Tensors are generalizations of vectors and matrices.
<cite>[[http://maths.dur.ac.uk/users/kasper.peeters/pdf/tensor_en.pdf|Introduction to Tensor Calculus]] by Kees Dullemond & Kasper Peeters</cite></blockquote>


</tabbox>