1. The problem statement, all variables and given/known data Find acceleration for a general point (x, y) at time t, in the velocity field u = (y, t-x) 2. Relevant equations Du/Dt = ∂u/∂t + (u⋅∇)u 3. The attempt at a solution ∂u/∂t = (0, 1) (u⋅∇)u = [(y, t-x)⋅(∂/∂x, ∂/∂y)](y, t-x) = (0 + 0)(y, t-x) = (0, 0) Thus Du/Dt = ∂u/∂t + (u⋅∇)u = (0, 1) + (0, 0) = (0, 1) It seems correct but my lecturer has given a different example, for a different problem, in which he draws out the entire process (presumably for the sake of letting students follow every tiny step) but I think there are typos in his work and it's really confusing things for me. So I've stuck with what I believe to be correct, but would like to run it by you guys to see if things are all ok. Thanks! For reference, my lecturer's example is here - http://www1.maths.leeds.ac.uk/~kersale/2620/Examples/sol1.pdf - The part on the final page. It looks like he's written ∂/∂x in far too many places...?