TAM310hw08

# TAM310hw08 - e State the orthogonality of these polynomials...

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TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand Homework No.8 (Due Tuesday March 25) 1. The following equation is called Hermite’s equation: y pp - 2 xy p + 2 py = 0 (1) a. Obtain a solution to eq.(1) by power series. b. Find values of p such that eq.(1) has polynomial solutions. c. Find the ±rst 5 resulting polynomials. Normalize such that the leading coe²cient is 2 m , m = 0 , 1 , 2 , 3 , ··· . d. Put eq.(1) in Sturm-Liouville form.
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Unformatted text preview: e. State the orthogonality of these polynomials on the interval-∞ < x < ∞ . 2. The following PDE governs heat ³ow with convection: ∂u ∂t = k ∂ 2 u ∂x 2 + V ∂u ∂x 3a. Show that the x ODE obtained by separation of variables is not in Sturm-Liouville form. 3b. Solve the initial-boundary value problem: u (0 , t ) = 0 u ( L, t ) = 0 u ( x, 0) = f ( x )...
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