week7-hw - R , the image f ( R ) is also a rectangle, then...

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Homework, week 7 1. (BC, p. 286), 1(for grade), 2, 3 (hint: start with the second integral), 5 (for grade). 2. (BC, p. 296), 1, 6 (for grade). 3. (for grade) Verify that f ( z ) = z k is a one-to-one analytic mapping in a neighborhood of any z 0 6 = 0 ( k 6 = 0 is an integer). 4. (a) Prove that a linear function maps polygon to a polygon. (b) Prove that if f is an entire function and for some rectangle
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Unformatted text preview: R , the image f ( R ) is also a rectangle, then f is linear. 5. (for grade) Describe the image of the upper half plane under a mapping of the form f ( z ) = az + b cz + d where a,b,c,d are real and ad-bc < 0. 6. Find a formula for all conformal automorphisms of the upper half plane. 1...
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