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hw8 - resulting complex integral as the contour expands 3...

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MAE294B/SIO203B: Methods in Applied Mechanics Winter Quarter 2010 http://maecourses.ucsd.edu/mae294b Homework VIII Due March 4, 2010. Questions with a star have a numerical/plotting component. 1* Discuss the branch cut structure of f ( z ) = 2 - z 2 + 1 . You will find there are several choices. Plot the real and imaginary parts of f ( z ) using Matlab for these choices. 2 Compute Z 1 - 1 d x x 2 - 1 by considering a closed contour surrounding the branch cut and examining the behavior of the
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Unformatted text preview: resulting complex integral as the contour expands. 3 Let p ( z ) be a polynomial with only simple poles. Explain how to use the integral I 1 = Z C z p ( z ) p ( z ) d z to ﬁnd the roots of p ( z ) . [Hint: the similar integral I was discussed in class.] 4 Show that Z 2 π cos θ + 1 cos 2 θ + 4 d x = π √ 5 using contour integration. 1...
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