EGM4313HW14 - Page 725, problem 9: 1 is singular when e z z...

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Page 725, problem 9: 1 1 z e is singular when 12 z e z ni with a simple pole. 22 ( 2 ) 1 R lim lim 1 1 zz z ni z ni z ni esidue ee Page 725, problem 10: 2 2 0 ,2 . z iz z i i Therefore simple poles at z i i Residue at zi is 4 () 33 ii i . Residue at 2 is 4 (2 ) 16 . i i i Page 725, problem 11: 3 rd order pole at 2 2 . 1 1 1 lim 2! 2 2 d Residue e e dz Page 725, problem 21: 2 4 6 2 4 6 5 5 3 45 5 1 2 ( ) ( ) ( ) cos( ) 1 2! 4! 6! cos( ) 1 2! 4! 6! cos( ) (2 ) 4! 12 z z z z z z z z z z z z dz i i z Page 725, problem 23: Simple pole at 1/ 3. z 2 2 1/3 30 23 5 2 3(2 1) z Residue z Second order pole at 1/ 2. z
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2 1/2 2 2 1 30 23 5 1 4(3 1) 2 30 23 5 1 (2 )(2 ) 5 (2 1) (3 2 z z d z z Residue dz z zz dz i i Page 733, problem 8: 2 2 0 1 1 11 8 2sin( ) 8 1 (8 ( )) d dz dz z iz iz z iz There is a simple pole at
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This note was uploaded on 12/15/2011 for the course EGM 4313 taught by Professor Mei during the Fall '08 term at University of Florida.

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EGM4313HW14 - Page 725, problem 9: 1 is singular when e z z...

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