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Homework 12 Key

Homework 12 Key - Math 335 HW 12 Due Wednesday 11/20 5:15pm...

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Math 335 HW 12 NAME: _______________________________________ Due Wednesday 11/20 5:15pm Practice Problems (Do not turn in.) Sec 12.3 #11, 15, 19 Sec 13.1 #1, 3, 11, 13 Print out this page and write all answers directly on this worksheet. Show all work. Your answers must be clear and legible. All pages must be stapled. 1.) [5 points] Find the Fourier series on gG±,±² for the top-hat function ³g´² µ ¶ 0 ´ · G2 1 G 2 ¸ ´ ¸ 2 0 ´ ¹ 2

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2.) [8 points] Classify each 2nd order PDE below as hyperbolic, parabolic, or elliptic. Show some work to justify your answer. a.) 2 g G ± G ³ 5 g G ± g²g´ µ g G ± G µ 6 ³ 3 µ 4¶ · 16 b.) ´´ µ ¶ ² · 3¶ c.) ²² · ³2¶

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