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### 611s2002_assign03

Course: MTH 611, Fall 2008
School: Oregon State
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Word Count: 200

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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 &lt; 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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Oregon State - MTH - 611
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Oregon State - MTH - 611
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Oregon State - MTH - 611
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