Tensor theory is extremely useful in advanced engineering theory. It is used to help describe or model many natural phenomenon such as: physical forces, potential fields, particle or control element motion, wave propagation, etc.
Constructions notes:
Specific examples are:
aeronautical engineering
Navier-Stokes equations Presented in partial differential equation form.
dynamics of systems of rigid (assumed incompressible) bodies and particles
stress and strain within elastic bodies
electromagnetics Maxwell's Equations
Equation (1) zr=zr(a,t) where a stands for the set of 3 labels representing the 3 dimensions or axis of Euclidean space ... xi,xj,xk.