MATH 241 Midterm: MATH 241 UPenn 241Fall13mkupSolutions Exam
Document Summary
1 (2) 10 points the function u(r, ) describes the steady state temperature distribution in a thin plate. R shaped as an anulus with outer radius 2 and inner radius 1. That is: what must the value of c be so that the boundary value problem will have a solution. 2u = 0 ur(1, ) = 2 ur(2, ) = c sin2(3 ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (b) (6 points) find the general solution u(r, ), you don"t need to compute the coe cients. Answer: (a) c = 2. (b) u(r, ) = a0 + b0 ln r + Xm=1 (am,nrn cos m + bm,nr n cos m + cm,nrn sin m + dm,nr n sin m ) 2 (3) 10 points denote by g(x) the fourier sine series of the function ex on the interval [0, 1], that is, ex . Decide whether the following statements are true or false.
