TAM310quiz01

# TAM310quiz01 - Compute c and c 1 4 Using separation of...

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TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand Quiz No.1, Feb. 5, 2008 CLOSED BOOK. NO CALCULATORS. SHOW ALL WORK! 1. Find the general solution: ¨ x + 2 ˙ x + 5 x = 0 2. Find all possible eigenvalues λ n and associated eigenfunctions y n ( x ): y pp + 2 y p + λy = 0 , y (0) = y (1) = 0 Hint: you may assume that λ > 1. 3. It is desired to expand the function f ( x ) = 1 on the interval 0 x 1 in a Fourier series: f ( x ) = 1 = s n =0 c n cos nπx
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Unformatted text preview: Compute c and c 1 . 4. Using separation of variables on the following PDE, obtain 2 ODE’s. DO NOT SOLVE the ODE’s. ∂ 2 u ∂x 2 + ∂ 2 u ∂x∂y + ∂u ∂y = 0 5. Find u(x,y): ∂ 2 u ∂x 2 + ∂ 2 u ∂y 2 = 0 on 0 < x < 1 and 0 < y < ∞ . Boundary Conditions: u = 0 when x = 0 ∂u ∂x = 0 when x = 1 u = sin πx 2 when y = 0 u → 0 as y → ∞...
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