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Homework 11 (MATH 1199 Fall 2019)
1. Let C be a contour that surrounds all of the poles. Use the residue theorem (and the "shortcut theorem" to find residues) to compute the integral of...
(a) f(z)=ezcos(z)z2+1
(b) f(z)=z2sin(z)(z+1)2
(c) f(z)=cos(z)sin(z)z2+2z+1

2. Recall that the inversion integral for the Laplace transform of a function F with poles at z1,,zn is f(t)=12πiCF(z)eztdz, where C is a contour around the poles. Use the inversion integral to invert...
(a) F(z)=1z2+9
(b) F(z)=zz2+4
(c) F(z)=1(z+a)2(z+b)2