Chapter 13

Dressing Up Functions with the Taylor Series

In This Chapter

arrow Understanding elementary functions

arrow Seeing power series as polynomials with infinitely many terms

arrow Expressing functions as a Maclaurin series

arrow Discovering the Taylor series as a generalization of the Maclaurin series

arrow Approximating expressions with the Taylor and Maclaurin series

The infinite series known as the Taylor series is one of the most brilliant mathematical achievements you’ll ever come across. It’s also quite a lot to get your head around. Although many calculus books tend to throw you in the deep end with the Taylor series, I prefer to take you by the hand and help you wade in slowly.

The Taylor series is a specific form of the power series. In turn, it’s helpful to think of a power series as a polynomial with an infinite number of terms. So, in this chapter, I begin with a discussion of polynomials. I contrast polynomials with other elementary functions, pointing out a few reasons mathematicians like ...

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