TAM310hw03

TAM310hw03 - that can possess the following solution y =...

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TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand Homework No.3 (Due Tuesday Feb.12) 1. Derive 2 u in circular cylindrical coordinates by using the chain rule, starting with 2 u = u xx + u yy and applying the transformation x = r cos θ , y = r sin θ . 2. Same question as 1. above, except v = x + y, w = x 2 . That is, starting with 2 u = u xx + u yy , use the chain rule to ±nd 2 u in v, w coordinates. 3. The order of an ODE is the order of the highest derivative that appears in it. For example, y pp + y = 0 is second-order, and y ppp = 1 is third-order. a) What is the lowest order homogeneous constant coe²cient linear ODE
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Unformatted text preview: that can possess the following solution: y = sin x + e x + cos 2 x b) Find such an ODE that has this solution. 4. For what value of β does a solution exist to the following boundary value problem: d 2 φ dx 2 + dφ dx = 1 (1) dφ dx = 1 , x = 0 (2) dφ dx = β, x = L (3) 5. Find the general solution of these three Euler equations: a) x 2 y pp-3 x y p + 4 y = 0 b) x 3 y ppp + 6 x 2 y pp + 7 x y p + y = 0 c) x 2 y pp + x y p + 9 y = 0...
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This note was uploaded on 05/30/2009 for the course TAM 310 taught by Professor Phoenix during the Spring '08 term at Cornell.

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