Mathematics 317 T2Assignment#9 - Mathematics 317T2 Assignment#9 due Wednesday 1 Verify the divergence theorem when F = xi yj zk and is the closed

Mathematics 317 T2Assignment#9 - Mathematics 317T2...

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Mathematics 317T2 Assignment #9 due Wednesday, March 25, 2010 1. Verify the divergence theorem when kjiFzyx=and σis the closed surface bounded by the cylindrical surface 122=+yxand the planes z= 0, z= 1. 2. Suppose Eis conservative in the domain D. Then ϕ-∇=Ein Dfor some potential function ).,,(zyxϕSuppose ),,(zyxρand div E are both continuous in D. ∫∫∫∫∫=RdVzyxd),,(4ρπσSEfor any region R in Dbounded by a surface σ. that πρϕ42-=in D3. Let ),,(zyxFbe a continuously differentiable vector field defined on a domain Let R be a region in D bounded by the surface
Suppose Show . D .
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