MATH 301 Study Guide - Midterm Guide: Branch Point, List Of Zeppelins
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Math 301 (201) final examination - april 2005. The ow eld given by a source located at z = 1 is modi ed by the introduction of an in nite barrier at x = 0. Hint: you should consider using a contour that includes the ray = 2 . 3 . (b) by integrating around the nite branch cut [ 1, 1] (and using symmetry), evaluate. 2 (1 + x2) (c) show by considering the two cases x > 0 and x < 0 that p. v. z ei x. 2 1 d = sin|x| . {|z 1| < 2} {|z + 1| < 2: [20] (a) find a conformal mapping w = f (z) that takes the region into a portion of the right half plane. Draw rough sketches of the regions in both the z and w planes. It might be useful to check the image of z = 0. (b) find (x, y) that satis es.
