## ABSTRACT

Three numerical operations — differentiation, quadrature, and the finding of roots — are central to most computer modeling of physical sys tems. Suppose that we have the ability to calculate the value of a function, / (# ) , at any value of the independent variable x. In differentiation, we seek one of the derivatives of / at a given value of x. Quadrature, roughly the inverse of differentiation, requires us to calculate the definite integral of / between two specified limits (we reserve the term “integration” for the process of solving ordinary differential equations, as discussed in Chap ter 2), while in root finding we seek the values of x (there may be several) at which / vanishes.