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.