Constructions notes:

- A
^{i'}^{j'}_{k'}= x^{i'}_{i}x^{j'}_{j}y^{k}_{k'}A^{i}^{j}_{k}

- Aeronautical engineering
- Navier-Stokes equations Presented in partial differential equation form.
- Vorticity is an important quantity in various research, modeling and design calculations regarding lift, drag, and propulsion. It is a tensor quantity defined as: insert gif here when available.
- Continuum mechanics
- dynamics of systems of rigid (assumed incompressible) bodies and particles
- stress and strain within elastic bodies
- electromagnetism Maxwell's Equations
- Hydrodynamics

- Assume the fluid consists of particles which can be individually tracked as they move in relation to Euclidean 3-space. Thus an individual particle can be tracked as it moves.
- We shall use rectangular cartesian coordinates to describe our Euclidean 3 space .... z
_{r} - In the Lagrangian method, all particles are then described by: