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# HW10 - ∂ ∂ ∂ ∂ y u x u y u y x u x u(ii Use...

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ME 391: FALL 2007 HW 10 (Due Date: Dec. 5, 2007) 1. Find the Fourier series of ) ( x f on the interval (-5, 5). < + < < - = 5 0 , 1 0 5 , 1 ) ( x x x x f 2. Expand the given functions in an appropriate cosine or sine series. (i). < + < < - - = π π x x x x x f 0 , 1 0 , 1 ) ( (ii). , ) ( 2 2 x x f - = π π π < < - x 3. (i). Find the half-range cosine and sine expansions of the given function. < < < = 1 2 1 , 0 2 1 0 , 1 ) ( x x x f (ii). Expand , 2 ) ( x x f - = 2 0 < < x in a Fourier series by defining it on 0 2 < < - x as ) 2 ( ) ( + = x f x f . 4. (i). Classify the given partial differential equations as hyperbolic, parabolic, or elliptic. (a). 0 5 3 2 2 2 2 2 = + + y u y x u x u (b). 0 6 2 2 2 2 2 2 = -
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Unformatted text preview: ∂ ∂ + ∂ ∂ y u x u y u y x u x u (ii). Use separation of variables to find, if possible, a product solution for the following partial differential equation. u y u x u = ∂ ∂ + ∂ ∂ 2 2 2 2 Assume the separation constant to be positive. 5. Practice Problems (do not submit for grading) Exercises 12.2: Problems 2, 3, 6, 11 Exercises 12.3: Problems 1, 2, 7, 23, 24 Exercises 12.4: Problems 1, 5 Exercises 13.1: Problems 1, 6, 11, 17, 19, 26...
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