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# 374chw8 - HW#8 Phys374Spring 2008 Due before class Friday...

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HW#8 —Phys374—Spring 2008 Prof. Ted Jacobson Due before class, Friday, April 11, 2007 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374b/ [email protected] 1. (a) Evaluate z dz along the following two contours connecting - 1 to 1: (i) from - 1 to 1 along the real axis, and (ii) along the semicircle of radius 1 in the complex plane. (Do both contour integrals explicitly. Use the polar angle as the variable of integration for (ii), and use x = Re ( z ) as the variable of integration for (i).) Explain how you could have known the two integrals would agree without even evaluating them. (b) Repeat part (a) for the integral z * dz, and explain why the two contour integrals do not agree in this case. [7+3=10 pts.] 2. Fluid flow and analytic functions : Problem 16.3 c,d,e,f [2+3+3+2=10 pts.] 3. Vortex : The velocity potential for a point source of fluid flow is given by the real part of h ( z ) = k ln z (where k is a constant), as shown in the previous problem. Show that the imaginary part of h ( z ) is the velocity potential for a point vortex. Do this by

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374chw8 - HW#8 Phys374Spring 2008 Due before class Friday...

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