Clairaut's theorem on equality of mixed partials: Difference between revisions

Revision as of 00:28, 13 February 2012

Statement

Suppose $f$ is a real-valued function of two variables $x,y$ and $f(x,y)$ is defined on an open subset $U$ of $\mathbb {R} ^{2}$ . Suppose further that both the second-order mixed partial derivatives $f_{xy}(x,y)$ and $f_{yx}$ exist and are continuous on $U$ . Then, we have:

$\!f_{xy}=f_{yx}$

on all of $U$ .

Revision as of 00:24, 13 February 2012 (view source) Vipul (talk \| contribs) (Created page with "==Statement== Suppose <math>f</math> is a real-valued function of two variables <math>x,y</math> and <math>f(x,y)</math> is defined on an open subset <math>U</math> of <math>...")		Revision as of 00:28, 13 February 2012 (view source) Vipul (talk \| contribs) No edit summary Newer edit →
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			{{commuting operators}}
	==Statement==		==Statement==