hw2 by xuyuzhu


									                      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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