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611s2002_assign03
Course: MTH 611, Fall 2008School: Oregon State
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TH M 611 A SSIGNMENT 3 Due: Monday April 29, 2002 Bent E. Petersen petersen@math.orst.edu Contour Integrals Use this page as cover sheet stapled onto your submission, or do all your work on this page if there is sufficient room. Name: Problem 1. Let be a closed rectifiable curve in C. Let w C, w traj (). Suppose we make some rough / dz estimates of the integral z-w and we find dz - 18i < 5. z-w...
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TH M 611 A SSIGNMENT 3 Due: Monday April 29, 2002
Bent E. Petersen petersen@math.orst.edu
Contour Integrals
Use this page as cover sheet stapled onto your submission, or do all your work on this page if there is sufficient room.
Name: Problem 1.
Let be a closed rectifiable curve in C. Let w C, w traj (). Suppose we make some rough / dz estimates of the integral z-w and we find dz - 18i < 5. z-w
Compute the winding number Ind (w) of about w.
Problem 2.
Let f (x + iy) = x3 + iy 3 and let (t) = t + it2 for 0 t 1. Compute f (z) dz.
Problem 3.
Let : [a, b] C a be rectifiable curve. Compute the contour integral ez dz.
(Note need not be closed.)
Problem 4.
Let : [a, b] C be a rectifiable curve. Compute the contour integral sin z dz.
(Note need not be closed.)
Problem 5.
know
Let : [a, b] C be given by (t) = eit for 0 t 1 so is a parametrizaton of the unit circle. We 1 dz = 2i. z
Compu...
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