208ss216-ex2 - Math 208, Summer II, 2016, Exam # 2 July 28,...

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Math 208, Summer II, 2016, Exam # 2July 28, 20161. State the Cauchy Integral Formula, being careful to include the conditions on the func-tionf(z).(10 points)Letf(z)be an entire function so that there is a positive numberAfor which|f(z)| ≤A|z|for allzCwith|z|>1. Show thatf(z) =az+bfor somecomplex numbersaandb.(10 points)2. Find the following contour integrals.(20 points)(a)ZCez(z-1)2. whereCis the circle|z|= 2.(b)RCsin(z)dz,whereCis the unit circle|z|= 1, with the positive orientation.(c)ZCz dzz2-1, whereCis the circle|z-1|= 1. d the Taylor series, centered at the pointindicated, of the following functions
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Term
Fall
Professor
CAO
Tags
Math, Cauchy Integral Formula

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