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This is the question I got on my final assignment (Calculus III):

Evaluate the surface integral

\begin{equation} \int \int_S xy \; \; dy\wedge dz - yz \; \; dz\wedge dx + xz \; \; dx\wedge dy \end{equation}

Where $S$ is the part of the plane $x+y+z=1$ lying in the first octant. Use $x$ and $y$ as parameters.

I am quite confused. I asked around and someone told me that this is also the symbol for something called the Wedge product, which I've not heard of before and appears in neither my calculus textbooks (Stweart's and Div Grad Curl) nor any of my Linear Algebra books.

From what I saw online, I still don't understand how it would make sense in this equation.

Is this a typo? Seems like a strange typo. Should it just read:

\begin{equation} \int \int_S xy \; \; dydz - yz \; \; dzdx + xz \; \; dxdy \end{equation}

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    I don't think thats a typo. Look for "differential form" in your textbook.2011-11-27
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    **Should it just read:** Yes, almost, but you have to take into account the sign. One would think, though, that notation in the assignment should be in the textbook...2011-11-27
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    Would you be able to evaluate the last expression?2011-11-27
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    @PZZ Differential forms: It's not in the index of either, and I don't see this notation anywhere in the chapter... I guess I must've missed a lecture on this.2011-11-27
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    @fakaff check out Principles of Mathematical Analysis by Rudin. The chapter on integration of differential forms has it. I think Rudin also uses this notation.2011-11-27

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