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Math 121A Math for physics Sciences Homework 4
Due Monday in class.
1. Taylor expand (�+1)(�+2)(z+1)(z+2) around �=3z=3.
2. Laurent expand 1/[(�−1)(�−2)]1/[(z−1)(z−2)] around �=1z=1. And do it again, this time around �=2z=2.
3.Compute ∫02�1/(�(�))��(�).∫02π1/(z(t))dz(t). for the following three contours (a) For �∈[0,2�]t∈[0,2π], let �(�)=���z(t)=eit.
(b). For �∈[0,2�]t∈[0,2π], let �(�)=��2�z(t)=ei2t.
(c ). For �∈[0,2�]t∈[0,2π], let �(�)=�−��z(t)=e−it.
Boas, Ch 14, Section 3, #4, 6