We recall the continuity and Euler momentum equations in Eulerian form, derive the material derivative \(\mathrm{d} \mathbf{v} / \mathrm{d} t=\partial_t \mathbf{v}+(\mathbf{v} \cdot \nabla) \mathbf{v}\), and explain how Eulerian field descriptions relate to Lagrangian particlebased descriptions via \(\rho(\mathbf{x}(t), t)\).