Can anybody answer this question:

I typed Euler's Criterion into google and near the end of the page, I found a link that said "What is "Euler's Criterion" in plain simplified english Text …" I thought this would be a good link to explore because in math, it really helps me to think about the theorems in English and pictures, rather than trying to understand formulas. This page turned out to be a thread (where I think just about anybody can type in, so don't take it to be true). Anyway, they were talking about Euler's Criterion in terms of differentials, and other crazy calculus-looking words. So here's my question: is there more than one Euler's Criterion, or is there a more in-depth-analysis way of looking at Euler's Criterion? And if the second part is true, can anybody make any sense of it?

Question about Euler's Criterion

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Question about Euler's Criterion

Angela Dodge 16 Mar 2009 16:28

I can't come up with anything right now, but can you post the thread you were looking at?

http://www.physicsforums.com/archive/index.php/t-242628.html

I think that's the link she was referring to.

I tried searching for it, and I was finding the equation with partial dirivatives usually is referred to as "Euler's Criteria for Exactness"

Euler's criteria of exactness says,

If a variable, call it $f$, is a property of a system iff

(1)\begin{align} \frac{\partial ^2f}{\partial x\partial y}=\frac{\partial ^2f}{\partial y\partial x} \end{align}

http://www.bmb.psu.edu/courses/bmb428/problemsets/bmb428_problemset02.pdf

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