MATH 321 Study Guide - Midterm Guide: Fourier Series, New Zealand, Legendre Polynomials
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De ne (a) r b a f (x) d (x) (b) a self adjoint algebra of functions (c) the fourier series of a function. Give an example of each of the following, together with a brief explanation of your example. Let f be a continuous function on ir. Suppose that f (x) exists for all x 6= 0 and that f (x) 3 as x 0. Continued on page 6 for p and s(p, t, f ) = pn. S(p, t, f ) z b a (cid:12)(cid:12)(cid:12)(cid:12) f (x) dx(cid:12)(cid:12)(cid:12)(cid:12) Suppose that the function f : [a, b] ir is di erentiable and that there is a number d such that. |f (x)| d for all x [a, b] . Let p = {x0, x1, , xn} be a partition of [a, b], t = {t1, , tn} be a choice i=1 f (ti)[xi x 1] be the corresponding riemann sum. Dkp k(b a) where kp k = max.
