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basic_tools:tensor_calculus

Tensor Calculus

Intuitive

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.http://qr.ae/TUTNzc

Concrete

Recommended Books

Abstract

The motto in this section is: the higher the level of abstraction, the better.

Why is it interesting?

Tensor calculus is a technique that can be regarded as a follow-up on linear algebra. It is a generalisation of classical linear algebra. In classical linear algebra one deals with vectors and matrices. Tensors are generalisations of vectors and matrices. Introduction to Tensor Calculus by Kees Dullemond & Kasper Peeters

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