MATH 316 Lecture Notes - Implementation Force, Unit Circle, Entire Function
13 Dec 2012
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Solution of homework assigned on february 5, 2009 due february 17, 2009. Problem 1 (from stein & shakarchi, pp. 30-31, #25). (a) evaluate the integral (cid:90) zndz for all integers n (positive, negative, or zero). Here is any circle centered at the origin with the positive (counterclockwise) orientation. (b) same question as before, but with any circle not containing the origin. Hint: use the parametrization z = a + rei for 0 2 for the circle of center a c and radius r > 0. Find a complex-valued function f ( ) of the real variable for 0 2 such that (cid:161) a + rei (cid:162)n d (cid:161) a + rei (cid:162) d d . F ( ) = d for 0 2 . Distinguish between the case where |a| < r and the case where |a| > r. (c) show that if |a| < r < |b|, then. 1 (cid:90) (z a)(z b) dz =
