MTH510-Assignment4

# MTH510-Assignment4 - concentration of dissolved oxygen at T...

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MTH 501/510 Assignment # 4 Fall 2011 DUE the week of November 28 (at the beginning of your Lab) 1. Consider the following data points: x -1 0 1 4 6 f ( x ) 2 2 0 42 170 (a) Use a Table for Divided-Diﬀerences (by hand) to construct the Newton interpolating polynomial for the data. Estimate f (3). (b) Use the M-ﬁle from Figure 17.7 to check your results in (a) with Matlab. As part of your answer, include a printout of the Matlab code used, or write the commands out by hand. You do not need to include the M-ﬁle from the Figure, unless you have made modiﬁcations to it. 2. Consider the following data points: x -2 -1 1 3 f ( x ) -5 -1 2 -2 Write down the Lagrange interpolating polynomial for this data and use it to estimate f (0 . 3). As part of your answer, write down the value for each of the terms of the interpo- lating polynomial when estimating f (0 . 3). 3. The following data deﬁne the sea-level concentration of dissolved oxygen for fresh water as a function of temperature: Temperature (degrees Celsius), T 0 4 8 12 o ( mg/L ) 14.6 13.2 11.8 10.9 (a) By hand, construct a linear spline to ﬁt the data, and use it to estimate the sea-level
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Unformatted text preview: concentration of dissolved oxygen at T = 6 degrees Celsius. (b) By hand, construct a natural cubic spline to t the data. Based on the spline, what is the sea-level concentration of dissolved oxygen at T = 6 degrees Celsius? (c) Write down the equations for the c i (by hand) for a clamped cubic spline with zero derivatives at the end knots. Do not solve the system, and do not nd the clamped cubic spline, just write down the equations for the c i . 4. Consider the integral 5 Z 2 e-3 x dx (a) Evaluate the integral using Simpsons 1/3 rule with n = 4. (b) What value of n would be required to estimate the integral with Simpsons 1/3 rule to guarantee an accuracy of 10-6 . 5. Do one iteration of Romberg integration to approximate 2 R 1 cos ( x 2 ) dx . Also compute the approximate percent relative error of your approximation....
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## This note was uploaded on 03/07/2012 for the course MTH MTH510 taught by Professor Dr.silvanailie during the Winter '12 term at Ryerson.

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