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Unformatted text preview: f ( z ) = 1 ( z-1)( z-2) (10 pts.) Obtain the Laurent expansion centered at z = 0 for each one of the following three regions: (a) | z | < 1, (5 pts.) (b) 1 < | z | < 2, (5 pts.) (c) | z | > 2 (5 pts.) [Hint: Re-express f using partial fractions.] 5. (25 pts.) Locate and classify all the singularities in the nite plane of f ( z ) = 1 z (exp ( z )-1) . (8 pts.) Calculate the residues at these singularities (8 pts.). Give the rst two terms of the Laurent expansion about z = 0 (8 pts.). Is the point at an isolated singularity? (1 pt.) Due at 5pm on Wed. October 28....
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This note was uploaded on 01/14/2010 for the course ACM 1 taught by Professor Prof during the Fall '09 term at Caltech.
- Fall '09