The tabular method for functions

The tabular method for functions

The analytic method of representing a function is primarily used in theoretical work, when it is a matter of general laws. In practical work, which requires the computing of a large number of particular values of different functions, an analytic presentation is often unwieldy, since it means carrying out all the necessary calculations in each case. To avoid this, particular values of the most commonly occurring functions are computed for a large number of particular values of the independent variables, and tables are compiled.
 For example, there are tables of values of the functions:

Such functions are constantly met with in practical work. Very useful tables have also been compiled for more complicated functions, such as Bessel functions, elliptic functions etc. There are further tables for functions of more than one variable, the simplest example being the ordinary multiplication table, i.e. a table of values of the function z = x*y for different integral values of x and y. Occasionally, the tables only give the function for particular values of the independent variables, adjacent to those values for which the function is required; in order to make it possible to use the tables in this case, various rules of interpolation exist; one such rule is given in school courses on using logarithmic tables (proportional parts). Tables have special importance when they represent a function, the analytic expression for which is unknown; this is the case when an experiment is carried out. Every experimental investigation aims at discovering hidden functional relationships, and experimental results are set in the form of a table, relating the different values of the magnitudes investigated in the experiment.

the source:

A COURSE OF Higher Mathematics VOLUME I. SMIRNOV.

By: Fady tarek