Numerical Methods for Partial Differential Equations

view for the Taylor’s series and the curve ﬁtting. Theorem 1.1. (Taylor’s Theorem). Assume that u2Cn+1[a;b] and let c2[a;b]. Then, for every x2(a;b), there is a point ˘that lies between xand c such that u(x) = p n(x) + E n+1(x); (1.1) where p nis a polynomial of degree nand E n+1 denotes the remainder deﬁned as p n(x) = Xn k=0 u(k)(c ...