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Unformatted text preview: . (Dont be alarmed - just apply Greens Theorem!) 4. (20) Let ~ F ( x, y, z ) = 2 y ~ i + 3 z ~ k , and let S be the surface x = u , y = v , z = 3 u + 2 with 0 u 1, 0 v 1. Let ~n be the upward unit normal to S . Find R S ~ F ~ndA . 2 5. (10) Let R be the box | x | 1, | y | 2, | z | 3. Use the Divergence Theorem to fnd R R ~r ~ndA , where ~r = x ~ i + y ~ j + z ~ k is the position vector, and ~n is the out ward unit normal. 6. (10) Let S be the surFace given by ~r = u ~ i + v ~ j + (1 3 u v ) ~ k , 0 u 1, 0 v 2, with upward unit normal, as seen From the positive z-axis. Let ~ F ( x, y, z ) = ( x z ) ~ i + ( x + y ) ~ j + ( y z ) ~ k Use Stokes Theorem to evaluate H S ~ F d~r . 3...
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This note was uploaded on 01/06/2012 for the course MATH 4038 taught by Professor Staff during the Summer '08 term at LSU.
- Summer '08