MATH 300 Study Guide - Midterm Guide: Medieval Commune, Iden, Ilog
Document Summary
Be sure that this examination has 12 pages including this cover. You will be graded on the clarity of your explanations as well as on the correctness of your answers. Find a branch of (1 + z)1/2 which is analytic except for z = x 1 and nd its derivative at z = 2. Evaluate the contour integral where c is the semicircle |z 1| = 1, im z 0 from z = 0 to z = 2. Find all entire functions f (z) that obey there is an integer n such that |f (z)| < |z|n + 1 for all (cid:8) z c (cid:12)(cid:12) |z| > 100 (cid:9) . 1 (2z 1)(z 2) (a) expand f (z) in a laurent series valid in an annular region that contains z = 1. [10] 7. (a) show that is an entire function. (b) evaluate. 1 z if z = 0 if z 6= 0.
