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Partial differential

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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
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article