The Chebyshev polynomials 7(x) are solutionsto the differential equations(I x 2 )y"xy'+n2 }' = 0 for n = 0, 1,2 Verify this fact for n = 0, 1, 2, 3

MATH 2450 WEEK 4 Curvature the reciprocal of the radius of the oscillating circle Flat Line Definition of Curvature R(t) if R(s) where ‘s’ is the arclength then k(s)= || T’(s) || Function If R(t) where ‘t’ is generic Main function: k(t) = || T’(t) || || R’(t) || Used but not as much as the above function k(t) = || R’(t) X R”(t) || || R’(t) || Used when x, y, or z is a nonspecific function or by themselves k(t) = | f ”(t) |