HW-1 - Fall 2010 Homework 1 EN 530.766 1) Consider the...

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Fall 2010 Rajat Mittal Homework 1 EN 530.766 1) Consider the following PDE (, ) xx xy yy x y abcdefg x Φ+Φ+Φ+Φ+Φ+ Φ = y . Transform the above equation from to ) , ( y x ) , ( η ξ and show that the transformed equation can be written as ) , , , , ( ηξ ηη ξη ξξ Φ Φ Φ = Φ + Φ + Φ H C B A obtain expressions for ,,,& ABC H 2) Classify and determine the characteristics of : a) 0 2 = yy xx yu x u 0 > y b) 0 2 2 2 = + + + yy y xy y x xx x u e u e u e Also plot the characteristics. Do not plot by hand; use MATLAB or any other
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