Definition:Rate of Change
Definition
The rate of change of a physical quantity is its (first) derivative with respect to an independent variable which is usually, but not exclusively, time.
Loosely speaking, it means how fast something changes, with a wider scope than change in physical displacement.
Time
When the independent variable of a rate of change is time, it is commonplace to take that fact for granted, and refer merely to its rate of change.
Rate of Increase
A rate of increase is a rate of change measured in a strictly positive direction.
Rate of Decrease
A rate of decrease is a rate of change measured in a strictly negative direction.
Hence a negative rate of decrease is a rate of increase.
Dimension
Let a physical quantity $P$ have dimension $\mathsf D$.
Then the rate of change of $P$ with respect to time has dimension $\mathsf {D T}^{-1}$.
Also see
- Results about rate of change can be found here.
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{VI}$: On the Seashore
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rate of change