Partial differential
From Encyclopedia of Mathematics
of the first order of a function in several variables
The differential of the function with respect to one of the variables, keeping the remaining variables fixed. For example, if a function 
is defined in some neighbourhood of a point 
, then the partial differential 
of 
with respect to the variable 
at the given point is equal to the ordinary differential 
at 
of the function 
in the single variable 
, i.e.
 |
 |
It follows that
 |
Partial differentials of order 
are defined analogously. For example, the partial differential 
of order 
of 
with respect to 
at 
is just the 
-th order differential of the function 
in the single variable 
at the point 
. Hence,
 |
 |
Comments
For references see Differential calculus and Differential.
How to Cite This Entry:
Partial differential. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Partial_differential&oldid=48133
Partial differential. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Partial_differential&oldid=48133
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article