hw2 - the resulting polynomials are proportional to the...

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Department of Chemical Engineering University of California, Santa Barbara ChE 230A Fall 2006 Instructor: Glenn Fredrickson Homework #2 Homework Due: Thursday, Oct. 12, 2006 1. Use the Gram-Schmidt procedure to construct a set of orthogonal polynomials over the interval - 1 x 1, starting from the monomials φ n ( x ) = x n , n 0 and using the conventional L 2 [ - 1 , 1] definition of the inner product. Show that
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Unformatted text preview: the resulting polynomials are proportional to the Legendre polynomials, P n ( x ), and are identically P n ( x ) if the normalization P n (1) = 1 is chosen. 2. Solve the following problems in your Riley, Hobson, and Bence text (3rd ed.): 12.8, 12.14, 12.16, 12.21, 12.26. You may want to use Mathematica to check your results....
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