BÄ°LKENT COMPLEX CALCULUS3pdf

B&Auml° - Date Friday NAME Time 9:00-11:00 ¨ Ozg¨uler& Sert¨oz STUDENT NO Math 206 Complex Calculus – Final Exam – Solutions

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Unformatted text preview: Date: May 18, 2007, Friday NAME:..................................................... Time: 9:00-11:00 ¨ Ozg¨uler & Sert¨oz STUDENT NO:..................................................... Math 206 Complex Calculus – Final Exam – Solutions 1 2 3 4 TOTAL 25 25 25 25 100 Please do not write anything inside the above boxes! PLEASE READ: Check that there are 4 questions on your exam booklet. Write your name on the top of every page. Show your work in reasonable detail. A correct answer without proper reasoning may not get any credit. Q-1) Evaluate the integral Z R cot z z 4 dz , where R is the positively oriented boundary of the rectangle whose corners are at the points 2 + 4 i ,- 2 + 4 i ,- 2- 4 i and 2- 4 i . Solution: There is only one pole at z = 0 in this region. The value of the integral is then equal to 2 πi times the residue of cot z z 4 at z = 0. We first find this residue: cot z z 4 = cos z (sin z )( z 4 ) = cos z ( z- z 3 6 + z 5 120- ··· )( z 4 ) = cos z (1- z 2 6 + z 4 120- ···...
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This note was uploaded on 11/08/2011 for the course MATH 332 taught by Professor Feritöztürk during the Spring '05 term at Bilkent University.

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B&Auml° - Date Friday NAME Time 9:00-11:00 ¨ Ozg¨uler& Sert¨oz STUDENT NO Math 206 Complex Calculus – Final Exam – Solutions

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