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Unformatted text preview: z for the function f ( z ) = 1 z 2 (1z ) and specify the regions in which these expansions are valid Ans : X n =0 z n + 1 z + 1 z 2 , (0 <  z  < 1); X n =3 1 z n , (1 <  z  < ) 5) BC p. 206 problem 6: Show that when 0 <  z1  < 2, z ( z1)( z3) =3 X n =0 ( z1) n 2 n +21 2( z1) 6) BC p. 239 problem 1: Find the residues at z = 0 of the functions ( a ) 1 z + z 2 ; ( b ) z cos 1 z ; ( c ) zsin z z ; ( d ) cot z z 4 ; ( e ) sinh z z 4 (1z 2 ) Ans ( a ) 1; ( b )1 / 2; ( c ) 0; ( d )1 / 45; ( e ) 7 / 6 7) BC p. 239 problem 2: Use Cauchys residue theorem to evaluate the integral of each of these functions around the circle  z  = 3 in the positive sense (counterclockwise contour) ( a ) ez z 2 ; ( b ) ez ( z1) 2 ; ( c ) z 2 e 1 /z ; ( d ) z + 1 z 22 z Ans ( a )2 i ; ( b )2 i/e ; ( c ) i/ 3; ( d ) 2 i 1...
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This note was uploaded on 03/30/2010 for the course PHYSICS 132 taught by Professor Staff during the Winter '06 term at UCLA.
 Winter '06
 staff
 Physics, Work

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