Question

42.(a) Solve for u(r, θ): u,( 1,0)-0, u(23)-40. That is, the region is an annulus betweenr 1 and r-2 HINT: First draw a picture of it, to get a look at the problem. Now, you should be able to readily get u(r, θ)-(A+B In r) (C+D6) + (Er"+FF") (Geosx8+ Hsinx8). Then, see that you have 2n-periodicity, so K n (n-1,2,..) and D-0, so u ( r, θ)-A" + B. In r + an infinite series with r's and θ's in it. But look at your picture; why should there be any 0 variation of u since there is complet e sy 0? Thus, it looks like all we will need is u(r, e) A'+ B' In r. Apply the two boundary conditions to ) soteval uhe Du ad Br und you're done and can get pizza and you're done and can get pizza.

Answer 1

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