374chw9 - HW#9 Phys374Spring 2008 Due before class Friday www.physics.umd.edu/grt/taj/374c Prof Ted Jacobson Room 4115(301)405-6020

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HW#9 —Phys374—Spring 2008 Prof. Ted Jacobson Due before class, Friday, April 18, 2008 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374c/ jacobson@physics.umd.edu Note : Be sure to fully justify the relation between the given integral and the closed contour integral you employ in the following problems. 1. Find the residues of the following functions at the given values of z : (a) ( z + z 2 ) - 1 at 0 and at - 1. (b) z - 2 ln(1 + 2 z ) at 0 (c) [ z 3 ( z + 2) 2 ] - 1 at 0 and at - 2. (d) cos z/ (2 z - π ) 4 at π/ 2 (e) ( z 2 + 1) - 3 at ± i . Hint : See the supplement for methods of evaluating residues. [3 × 5 = 15 pts.] 2. Consider the real integral Z -∞ dx ( x 2 + a 2 )( x 2 + b 2 ) where a and b are positive real numbers. (a) Evaluate the integral using contour integration assuming a 6 = b (so there are only simple poles). (b) Evaluate the integral using contour integration assuming a = b from the begin- ning (so the poles are of order 2), and then check that you recover the same
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This note was uploaded on 12/29/2011 for the course PHYSICS 374 taught by Professor Jacobson during the Fall '10 term at Maryland.

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374chw9 - HW#9 Phys374Spring 2008 Due before class Friday www.physics.umd.edu/grt/taj/374c Prof Ted Jacobson Room 4115(301)405-6020

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