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417_hw7 - a Find the maximum value of u in r ≤ 2 b...

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Homework #7–Due Tuesday, March 20 Do the following problems from section 2.5 of Haberman: 3b, 5a,d, 9, 10, 11 Also do the following problem, appearing in 6.3 of Strauss: Supplemental Problem: Suppose that u ( r,θ ) is a harmonic function in the disk D = { r < 2 } (in polar coordinates) and that u (2 ) = 3 sin 2 θ + 1 for r = 2. Without finding the solution, answer the following questions.
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Unformatted text preview: a) Find the maximum value of u in { r ≤ 2 } . b) Calculate the value of u at the origin. Reading: Haberman 2.5 Review: Vector calculus–In particular, review 2D and 3D versions of the Diver-gence Theorem, polar coordinates, spherical coordinates, surface integrals (espe-cially over a sphere)....
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