Exam 2 Sample Paper - Complex Variables | MATH 322, Exams of Mathematics

Download Exam 2 Sample Paper - Complex Variables | MATH 322 and more Exams Mathematics in PDF only on Docsity! MATH 322 CenpLex vARIABLES TésT 72 (sanPLE) NARE THIS 1§ A 90 mimuTE TEST, SHow ALL OF YeuR Worn, 102 POIWTS TOTAL, z-2 FIND ALL OF THE SIMGULARINES oF Frad, 1. (20 Powrs) rer Fear = FiwD LAURENT SERIES EXPANSIONS FOR Pad VALID On (a) O<l2le), tb) 12) >1, Amo coy O¢ 2-1] <), Fiwo THE RESIDUES oF fea aT Zz: 0 Awo 2:1, 2, (30 PowTs ) EACH oF THE FOLLOWING HAS A SimGuLARITY AT B= O, CLASSIFY THE SINGULARITY ( POLE OF SONE ORDER, ESSENTIAL, RENOVABLE ) AWO DETERNINE 7s RESIDUE , cay fay? 2 ow cb) Fad = Enh’ 3a* ce) Feays 4 2F 3. CIO Points) GIVE AN EXANPLE oF EACH OF THE FOLLQWOING (YOU NEED WoT VERIFY THAT YouR EXANPLE HAS THE REQUIRED PROPERNES ), Cay A NOWRATIONAL FUNCTION WITH A POLE oF ORDER 2 AT 22 5, th) A FUNCTION WITH AN ESSENTIAL SINGLLARITY aT 2 = |, 4c) A Femcnen wilh A SIMPLE PeLe aT 220 ANDO AN ESSENTIAL SIMGRLARITY AT 21. td) A FUNCTION WITH A NOMRENOVABLE SINGULARITY AT 222, BT wits Res rz) = 0, 20