Theorem 1.5(Newton Polynomial). Suppose that to, I1,..., IN are N+ distinct numbers in a, b]. There exists a unique polynomial PN()of degree at most N with the property that f(i)= PN(ifor j=0 The Newton form of this polynomial is Px(x)=a0+a1(x-x0)+…+aN(x-x0)(x-x1)…(x-xN-1),(1.69) where ak= f co, 21, ...,k], for k=0, 1,..., N