MATH 118R Midterm: MATH 118 Harvard

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15 Feb 2019
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This exam is open notes and open book: you may use any of your notes and the textbooks for this course. You may also use a reference on real analysis if you wish. That is, for which points z is lim. Where does the boundary of the rst quadrant go (with orientation): evaluate the following sums and integrals: d . 1 2a cos + a2 (with a c and |a| 6= 1); dx. 0 (a) z 2 (b) z (c) z (d) 1 (2z 1)(z 2) which converges inside the annulus 1. 2 < |z| < 2: find h z dz around (a) the boundary of an arbitrary rectangle and (b) the boundary of an arbitrary circle. |f (z)| > r. ) (a) show that f (z) has only a nite number of poles. (hint: you might start by considering the function g(z) = 1/f (1/z).