MAA 4402 Final: complex-final-part2-fall2015

• School: University of Florida
• Department: Mathematics-Analysis
• Course: MAA 4402
• Professor: All

Document Summary

Maa 4402/5404 fall 2015 final exam part 2. Your work should be written in a proper and coherent fashion, and in a way that any student in the class can follow your work. 51 points total: [2 + 6 = 8 pts] (a) state the cauchy-goursat theorem. (b) let c be the simple closed countour with positive orientation which is the circle |z| = 1. Sketch the countour c and the region on which f (z) is analytic. Show reason- ing: [2 + 6 = 8 pts] (a) state cauchy"s integral formula for derivatives. (b) find the following contour integral. Zc sinh 2z z 4 dz, where c is the simple closed circle |z| = 2 with positive orientation. [5 + 5 + 5 = 15 pts] In each of the following, write the principal part of the function at its isolated singular point and determine whether that point is a pole, an essential singularity or a removable singularity.