# Individual derivative

From AMS Glossary

## individual derivative

(

*Also called*material derivative, particle derivative, substantial derivative.) The rate of change of a quantity with respect to time, following a fluid parcel.For example, if φ( (where

*x*,*y*,*z*,*t*) is a property of the fluid and*x*=*x*(*t*),*y*=*y*(*t*),*z*=*z*(*t*) are the equations of motion of a certain particle of this fluid, then the total derivative,**u**is the velocity of the fluid and**∇**is the del operator), is an individual derivative. It gives the rate of change of the property of a given parcel of the fluid as opposed to the rate of change at a fixed geometrical point, which is usually called the local derivative. The term**u**·**∇**φ is called the advective term, expressing the variation of φ in a parcel moving into regions of different φ.