# hw5_97f - Homework#5 MEAM 501 Analytical Methods in...

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Homework #5 MEAM 501 Analytical Methods in Mechanical Engineering 1997 Fall 1. Suppose that the following is the coordinates of the eleven control points of the Bezier spline curve C in the three dimensional space R 3 . {0,0,0} {0.1, 0.870501, 0.938693} {0.2, -0.968673, 1.13874} {0.3, -1.71508, 0.323311} {0.4, -0.202442, -0.385068} {0.5, 1.25, 0} {0.6, -0.278835, 0.530376} {0.7, -3.25672, -0.613928} {0.8, -2.53949, -2.98535} {0.9, 3.15378, -3.40084} {1., 7.5, 0} (1) Compute the total length L of the curve C by applying an appropriate quadrature. (2) Obtain the tangent, normal, and bi-normal vectors at the point P on the curve, where P is the 20% point of the total length L of the curve C. To identify the location of the 20% point of the total length, you may use either the bisection or Newton method. 2. Approximate the function fx xx (29= -+ - (29 -∈ 2 11 0 10 1 ,, defined on the interval (-1,1) by using (1) Legendre polynomials and the least squares method, (2) trigonometric functions ( i.e. Fourier series approximation ), and (3) the Lagrange interpolation. Plot the approximation and the original function, and

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hw5_97f - Homework#5 MEAM 501 Analytical Methods in...

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