Abstract
This chapter describes the numerical differentiation and integration. A study is made of numerical methods of solving simple but very widely used problems of mathematical analysis, namely, differentiation and integration of functions. Differentiation and integration are special cases of functions. A new function or a certain number is placed in correspondence with each function of a certain functional space R. In many cases, the values of these functions cannot be found exactly by means of differential and integral calculus. Numerical differentiation is required if the function f(x) for which one must find the derivative is defined by tables or if the functional dependence between x and f(x) is highly complex. It is found that in the first case, the methods of differential calculus are inapplicable, while their use in the second case causes too many difficulties.
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