Numerical Methods
In applications we often have to find numerical values. In many cases, it is not possible to obtain exact values. In practice it is usually enough to obtain an approximate value, together with a bound for the error involved.
In this chapter, we consider three such problems—finding zeros of a real function, evaluating a definite integral and finding the solution of an initial value problem for an ordinary differential equation.
The methods are of two types—iteration and local approximation. In the former, we obtain a sequence of approximations, each depending on previous values. In the latter, we approximate the function on an interval by a polynomial function (usually constant, linear or quadratic).
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