Gradient
Definition
The arrow pointing steepest uphill — temperature's gradient tells heat which way to flow.
Symbol: ·
Technical definition
∇f is the vector of partial derivatives, pointing in the direction of greatest increase; its magnitude is the slope. Heat flows down −∇T.
Example
On weather maps, the pressure gradient force pushes wind from high to low pressure, perpendicular to the isobars.
Common confusion
The gradient is a vector, not just a slope number. It carries direction (steepest ascent) AND magnitude — forgetting the direction misses half the meaning.