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 φn (x) = xn , n ≥ 0 and using the conventional L2 [−1, 1] deﬁnition of the inner product. Show that the resulting polynomials are proportional to the Legendre polynomials, Pn (x), and are identically Pn (x) if the normalization Pn (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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