With example express gradient, divergence and curl in both cylindrical and spherical coordnates

Gradient is another word for "slope". The higher the gradient of a graph at a point, the steeper the line is at that point. A negative gradient means that the line slopes downwards. The video below is a tutorial on Gradients. Finding the gradient of a straight-line graph.

The polar angle is denoted by θ: it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by φ: it is the angle between the x-axis and the projection of the radial vector onto the xy-plane.