week5-hw - 1 z 2-z 4 and Laurent expan-sions about these...

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Homework, week 5 1. (BC, 178-179) 1(for grade), 2, 3, 6. 2. Suppose f → ∞ as z 0. Show that f has a pole at z = 0. 3. Find the range of the function e - 1 z as z varies through deleted disc 0 < | z | < 1. 4. Describe all singularities of 1 sin( z ) . 5. (for grade) Describe all singularities of sin( 1 z ) ( z - 1) 2 ( z 2 +1) 6. (BC, p. 248) 1; (BC, p. 205-206) 1-6. 7. (for grade) Find singular points of the function
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Unformatted text preview: 1 z 2-z 4 and Laurent expan-sions about these points. 8. Find partial fraction decompositions of 1 ( z-1) 2 ( z 4-1) (for grade) , z ( z-1)( z 2 + 1) 9. Find singularities, their type, and corresponding residues for functions 1 z 2 + z 4 , e 1 /z 1-z , 1 sin z , sin (1 /z ) 1...
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This note was uploaded on 05/03/2010 for the course MATH 185 taught by Professor Lim during the Summer '07 term at Berkeley.

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