# Differentiation and Integration

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## Abstract

In the solution of practical problems, one often encounters derivatives and integral of a function *f* defined in a certain interval. In many cases, the function *f* is so complicated that even the powerful tools of calculus are either difficult to apply or become totally infructuous. In other cases, *f* may be defined in a *tabular form*, to which the results of calculus do not apply. In such difficulties, numerical answers may be sought by **approximating** the function *f* by an **interpolating polynomial** \(\phi \) obtained from a table of values of *f*(*x*), which if not given, may be constructed from the analytical definition of *f*.

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© Springer Nature Singapore Pte Ltd. 2019