Theorem 1.5 (Newton Polynomial ). Suppose that o, J1,. N are N+1 distinct numbers in a, b]. There exists a unique polynomial PN(ar) of degree at most n with the property that 0.1.N The Newton form of this polynomial is PR(x)=a0+a1(x-m0)+…+aN(x-0)(x-x1)…(x-xN-1),(1.69 where ak=f C0, C1,., w, for k=0, 1,..., N