MAD 4401 Study Guide for Test 1

MAD 4401 Study Guide for Test 1 - MAD 4401 Keesling 1....

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MAD 4401 Study Guide for Test 1 Keesling Test on 9/21/11 1. Have the following programs debugged on your TI-89 and ready for use on Test 1. Lagrange for a vector of x values and a vector of y values Vandermonde matrix for a vector of points Newton Cotes coefficients for n + 1 points Evaluation of Newton Cotes Estimate for n + 1 points Romberg Integration Gaussian Quadrature 2. Estimate the following integrals using Newton-Cotes, Romberg Integration, and Guassian Quadrature. (a) sin( x ) dx 0 π (b) exp( x 2 ) dx 0 1 (c) 1 1 + x 2 dx 4 4 In each of these cases discuss the error in using the estimate. 3. Give the polynomial and sketch the graph of the Lagrange interpolating polynomial approximating the following functions using n equally spaced points on the given interval. (a) sin( x ) on the interval [0, ] (b) exp( x 2 ) on the interval [0,1] (c) 1 1 + x 2 on the interval [-4,4] 4. Let T n ( f ( x ), a , b ) be the composite Trapezoidal Rule estimating f ( x ) dx
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MAD 4401 Study Guide for Test 1 - MAD 4401 Keesling 1....

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