405q7 - MATH 405: Quiz 7 Name: November 6, 2006 1 1. Given...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 405: Quiz 7 Name: November 6, 2006 1 1. Given that the first 4 Legendre polynomials are P0 = 1, P1 = x, P2 = 2 (3x2 - 1), and 1 3 2 P3 = 2 (5x - 3x), represent the function f (x) = 2x as a Legendre expansion. 2. Consider a Sturm-Liouville equation for y(x) in the standard form d dx P (x) dy dx + Q(x)y = -R(x)y on the interval (0, 12) with P = x, Q = 5x2 , and R = x3 + 12. Given an arbitrary function g also defined on (0,12), which we can expand as g(x) = an yn (x), how would you determine the an ? Write an explicit formula in terms of the eigenfunctions yn . ...
View Full Document

Ask a homework question - tutors are online