Dressing Up Functions with the Taylor Series
In This Chapter
Understanding elementary functions
Seeing power series as polynomials with infinitely many terms
Expressing functions as a Maclaurin series
Discovering the Taylor series as a generalization of the Maclaurin series
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 ...