Oxford Calculus: Gradient (Grad) and Divergence (Div) Explained

University of Oxford Mathematician Dr Tom Crawford explains the gradient vector (Grad) and the divergence (Div) for scalar and vector functions. Test yourself with this accompanying FREE worksheet in Maple Learn.

We begin with the formal definition of the gradient vector (Grad) and a visualisation of what it represents for a multivariable function. We then look at some examples with explicit calculation and 3D plots. The Divergence (Div) of a vector function is then introduced – both as an equation and via the physical interpretation of what it represents. We calculate the divergence for several vector fields and then show where the notation ‘Grad Dot F’ comes from with a derivation. Finally, the link between Grad, Div and the Laplacian is explored.