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A problem set focused on vector calculus, including the computation of flux, the use of green's theorem, and the determination of curl and divergence. Students are expected to solve problems (1) and (2) involving the vector field f(x, y) and the curve e(t), as well as problem (3) concerning the vector field < 2xyz, x + y + z, xy + yz + zx >.
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Problem Set 30, Due
(1) Compute the flux of the vectorfield F (x, y) =< 2 y, 3 x > across the curve E(t) =< 3 cos(t), 4 sin(t) >, t ∈ [0, 2 π], both directly and by using the second form of Green’s theorem. (2) Why can we consider the second form of Green’s theorem to be the funda- mental theorem of calculus for functions of two variables? (3) Compute the curl and divergence of the vectorfield < 2 xyz, x + y + z, xy + yz + zx >.
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