MATH253 Chapter Notes - Chapter 1-24: Compact Space, Complex Analysis

• School: University of Alberta
• Department: Mathematics
• Course: MATH253
• Professor: Souvik Goswami

Document Summary

From james lewis"s lecture notes, with permission from the author. Example computation in contour integration, and theorems in com- plex analysis. C in the following 4 cases of counterclockwise c: (i) |z| = 2, (ii) |z + 3| = 2, (iii) |z| = 100, (iv) |z 100| = 1. 1 z3(z + 4) is not analytic are at z = 0 and z = 4, i. e. where the denominator vanishes. (i) 0 lies inside |z| = 2 whereas 4 lies outside |z| = 2. |z|=2 z3(z + 4) f (z) = 1/(z + 4) (z 0)3 dz (ii) 4 lies inside |z + 3| = 2 whereas 0 lies outside |z + 3| = 2. The answers for (i) and (ii) won"t change if we choose a small. 2! z + 4 (cid:18) 1 (cid:19)(cid:48)(cid:48) (cid:18) 1 (cid:19)(cid:48) (cid:12)(cid:12)(cid:12)(cid:12)z=0 (z + 4)2. |z+3|=2 dz/z3 z ( 4) dz z3(z + 4)