2313-in-class-Nov30

# 2313-in-class-Nov30 - F across S as a surface integral(of...

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MAC 2313, Fall 2010 — In-class problems 11/30 These problems are solely for your ediFcation, and will not be graded. You are encouraged to work on them in groups. 1 Let the surface S denote the cone z = r x 2 + y 2 for z = 0 to z = 2. Parameterize S in polar coordinates, that is, as a vector function r ( r, θ ). 2 Use a surface integral to compute the surface area of S . Recall that the formula for surface area is ii S | r r × r θ | dA . 3 Suppose that F = y 2 i - z j + x 2 k . Compute curl F . 4 Express the circulation of
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Unformatted text preview: F across S as a surface integral (of curl F Â· n ). You do not need to evaluate this integral, but you should simplify it as much as possible. 5 Parameterize the boundary of S , âˆ‚S , as a vector function r ( t ). 6 Use Stokeâ€™s Theorem to express the circulation of F across S as a line integral along âˆ‚S . You do not need to evaluate this integral, but you should simplify it as much as possible....
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