Langrangian description: one essentially follows the history of individual fluid particles (I understand this, it's like tracking a particle and find its position x=x(c,t) where c is the initial position at time t=0. ) So, an equation that gives the position of a particle in terms of its initial position and time t can be said the be described in Langrangian coordinate) Eulerian description: one concentrates on what happens at a spatial point x. (I also understand this, my teacher said it's like setting a fixed volume, and describe what happens inside this volume) (For example, maybe, the temperature at a point x, the pressure at a point x) I can understand what are the meanings of the two explanatinos in the parentheses. but, I don't really understand how the Eulerian description in the following equation!!! Here is the material derivative of following a fluid element DF/Dt = delF/delt + v . grad (F) where F is the physical property of the system. The book says that DF/Dt is the material derivative, and delF/delt is the advective derivative(which I think is Eulerian description) , I don't understand why the books say so? It's not so intuitive to me.