Vector Fields and the Vector Operators
When you place one end of a metal spoon in hot water, heat flows from the end submerged in water to the end that is not. The temperature at each point in that spoon when viewed collectively is a scalar field. If a temperature-camera were to capture this spoon, it would look like this. Each point in this scalar field defines a temperature value. It does not show direction at all. But when the gradient of this temperature field is taken, the slope reveals that path with the steepest climb or drop in temperature. ...