ABSTRACT
Certain mathematical functions may be represented as a power series, containing terms in ascending powers of the variable. The uses of Maclaurin's series include expressing mixed functions, containing some or all of trigonometric, exponential, algebraic and logarithmic terms, in a form where such techniques as Newton's method, or approximate integration, can be employed. At a more advanced level, such theories as Webb's buckling of struts are based on an understanding of Maclaurin's series. Some of the applications of Taylor's series are to such techniques as numerical differentiation, limits, small errors and the numerical solution of certain differential equations. Several methods exist of finding the approximate value of definite integrals. One of these is to express the function as a power series and then to integrate the terms of the power series. This method is particularly suitable for use with functions whose power series converge fairly rapidly, where evaluation of a few terms gives the required degree of accuracy.
