Introduction
In this Section we examine how functions may be expressed in terms of power series. This is an extremely useful way of expressing a function since (as we shall see) we can then replace ‘complicated’ functions in terms of ‘simple’ polynomials. The only requirement (of any significance) is that the ‘complicated’ function should be smooth ; this means that at a point of interest, it must be possible to differentiate the function as often as we please.
Prerequisites
- have knowledge of power series and of the ratio test
- be able to differentiate simple functions
- be familiar with the rules for combining power series
Learning Outcomes
- find the Maclaurin and Taylor series expansions of given functions
- find Maclaurin expansions of functions by combining known power series together
- find Maclaurin expansions by using differentiation and integration
Contents
1 Maclaurin and Taylor series2 The Maclaurin series
3 Differentiation of Maclaurin series
4 The Taylor series