Question

In addition, please make sure to also write your name and homework number on the first page of your solutions. P1*. Solve Laplace's equation inside a semicircle with 0 < < and with radius a, subject to the boundary condition u(a, b) = sin(e) and with the diameter (@= 0 and 0 = ) insulated.

please solve step by step

Answer 1

468,00) 2 20 + Ë (979 fan cosmet businna) - ni Hese a gn Tax cosnot bosince goa Laney 41870) 2 gote - na je 109 2 20 25 17. sin?o do S." 7-cb129) do, Jolio 2 1- 2 sinko to [- singon -( 0 [- Sin 27 -0-0). Zo (1-0) is [ao = 2 x page an 2 1 / 2 (*. cosno, sinto do o c* cosno(2-60520) do South S.* cornado-*s* cosnacuszodo [stinn gl." - seta pot cushocesso do ? BA ( sinna-sino ) -it 1.* cu mo cuero de 0-0) -as f, sosno wszoda siang 20 =) - 1 / 2 2 , if n=2 lo, otherwise 2 25 Jo sinnt zo anz2 a 1, if nza otherwise

osnon T sinnacosmodoro bnata sinno 1-60529) 40 to S.* sinodo-os sinno coseo do Feb [ cosme). - &qxO* zionownedo Stan feos hot woso) -0 sztani [1-441)", i ma wsnts=(un bn 2 din it n is odd lo, it nû eren 2X 418,0) = 1 + gz. (-44) casso & E T sinna n=1,3,5 488,0) 21 - 22 cos 20 + 6+ sino + sin30 +--- ) (Pege 2