MATH 241 Midterm: MATH 241 UPenn 241Fall 04MakeupAns Exam
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Math 241 makeup final answers: true false, true, false, true, false, false, false, false, true, short answer, 12, 2 i, ei . All the fourier coe cients are zero except for 7, the coe cient on cos 2x: 2, 3, 4. 3: the integrand has simple poles at z = i, i. Zc z2 4 z2 + 1 dz = 2 i( Answer: the integrand has a pole of order 2 at 2. [(z 2)2 ez (z 2)2 ] = lim z 2 ez = e2. Zc ez (z 2)2 dz = 2 i(e2) = 2e2 i: the integrand, which we think of as sin z. 2 , and 5 all odd multiples of z = 0 is a removable singularity and hence its residue is 0. The poles inside c are z cos z , has simple poles at 0 and. Similarly res( sin z z cos z , 3 .
