HW_05-10-F - x 0 2 4 6 9 11 12 15 y 5 6 7 6 9 8 7 10 5. The...

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ChE 348 Homework # 5 ____________________________________________Due: Thursday, 14 October 2010 Nonlinear System: Newton’s Method 1. Consider the nonlinear system, 1 9 1 2 1 9 1 2 = + + = + y x e y x e y x Take ( x 0 , y 0 ) = (1, 1) and do two iterations of Newton’s method ( by hand ); you should get ( x, y ) = (-0.4831, 0.2136) 2. Write a computer code to solve the following systems, using Newton’s method (a) 1 4 2 2 2 2 = = + y x y x True solutions: ) 5 . 1 , 5 . 2 ( ± ± (b) 96 . 1 4 . 0 4 4 2 2 2 = = + x x y y x One solution: (1.77017, 0.46543) 3. Find all solutions to the system 4 3 9 3 2 3 2 = = + y y x xy x Use each of the initial guesses ( x 0 , y 0 ) = (1.2, 2.5), (-2, 2.5), (-1.2, -2.5), (2, -2.5). Observe the solutions to which each of the initial guesses converge and the number of iterations performed. Comment on your results. Linear Regression 4. Use least-squares regression to fit a straight line to
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Unformatted text preview: x 0 2 4 6 9 11 12 15 y 5 6 7 6 9 8 7 10 5. The following data was gathered to determine the relationship between pressure and temperature of a fixed volume of 1 kg of nitrogen. The volume is 10 m 3 . T, o C -40 0 40 80 120 160 P, N/m 2 6900 8100 9300 10,500 11,700 12,900 Employ the ideal gas law pV = nRT to determine R on the basis of this data. Note that for the law, T must be expressed in Kelvins. Interpolation 7. Given the data x 1 2 3 5 7 8 f(x) 3 6 19 99 291 444 Calculate f(4) using Newtons interpolating polynomials of order 1 through 4 ( by hand) . Choose your base points to attain good accuracy. What do your results indicate regarding the order of the polynomial used to generate the data in the table. 6....
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This note was uploaded on 11/28/2010 for the course CHE 348 taught by Professor Chelikowsky during the Spring '08 term at University of Texas at Austin.

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HW_05-10-F - x 0 2 4 6 9 11 12 15 y 5 6 7 6 9 8 7 10 5. The...

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