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# Example of calculating a surface integral part 2

Example of calculating a surface integral part 2. Created by Sal Khan.

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• This video without cursor is a bit confusing for me, i don't know where sal talk about when he say:
"that guy" but without the cursor i don't know what he's talking about.
• I was just about to complain about the same issue. I'm not sure if the problem is with the HTML player versus flash or if the video file is missing the cursor.
• I thought that matrices had to be squared in order to take a determinant?
(1 vote)
• It is, we let the unit vectors < i , j , k > be the first row, then the other two vectors to be the 2nd and 3rd rows. Thus, it becomes a 3x3 matrix.
• At , he could have written (b+a*cos(t)) outside of determinant. Result would be the same, but there would be less writing, as you can divide one row (or a column) by some number, and than multiply determinant by the same number (in our case (b+a*cos(t)) )
(1 vote)
• Is it just me or can no one see the cursor in this and the previous video cause without it, it gets kind of hard to understand which term Sal is referring to when he says "this guy" and "that guy"
• Wait so why do we have to take the cosine of i hat? is i hat supposed to be x vector?
(1 vote)
• I find the approach of alternating + and - for sub-determinates confusing, and prefer to either actually copy the first column as an extra column to the right (I think that's how I was taught long ago), or to just think of it as being there, so the pattern of the operation always stays the same (upper left x lower right) - (upper right x lower left) in each case. I think that's also consistent with the Levi-Civita symbols, which I don't quite understand, but look like lower case epsilon, and through some symmetry rules that determine which indices are -1, 1 or 0, apparently prescribe the indices in a compact way so that the cross product can be represented as a simple summation, and also lead to some (apparently) useful identities when combined with the Kroneker delta operator for the dot product. So not a question I guess. More of a comment, but I would like to have the Levi-Civita symbols explained. The source I have is completely cryptic and basically fails, though i*(A2B3-A3B2)+j*(A3B1-A1B3)+k(A1B2-A2B2) is the outcome.
(1 vote)
• Actually, I consider that method unnecessarily tedious and open to confusion, and that is the way my Calc III professor uses. It's easier just to know that the j vector component is negative, and evaluate a 3x3 matrix normally, which is the way I learned it in Engineering Statics.
(1 vote)
• Hello friends, I have an uneasy feeling about the way the computation is going. Sal created a parameterization of the torus in a left handed coordinate system and now he is taking a cross product which I think is defined only for a right handed coordinate system. In fact, the cross product essentially defines what is a right handed coordinate system. I am confident a better mathematician than I will suggest that it all comes out OK in the end, but I would be very reluctant to proceed in this way. Can anyone tell me why I should not be concerned? Best wishes.
(1 vote)
• what are those, adidas or nike or what?