My book is going through a proof on exact differential forms and the test to see if they're exact, and I'm lost on one part of it.(adsbygoogle = window.adsbygoogle || []).push({});

It says:

If $$M(x,y)dx + N(x,y)dy = \frac{\partial F}{\partial x}dx + \frac{\partial F}{\partial y}dy$$ then the calculus theorem concerning the equality of continuous mixed partial derivatives $$\frac{\partial }{\partial y}\frac{\partial F}{\partial x}=\frac{\partial }{\partial x}\frac{\partial F}{\partial y}$$ would dictate a "compatibility condition" on the functions ##M## and ##N##: $$\frac{\partial}{\partial y}M(x,y)=\frac{\partial}{\partial x}N(x,y)$$

What does this mean? What is the "calculus theorem concerning the equality of continuous mixed partial derivatives" it talks about?

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# I Question About Exact Differential Form

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