We begin our study of Taylor Series by looking at each half of the phrase individually - first we study (finite) Taylor polynomials. Then, before we extend them forever, we look at how series with a variable behave.
- Section 10.1: With this section, we begin the material for which the previous chapter was an introduction. With Taylor Polynomials, we will extend the idea of linear approximations as well as we can.
- Section 10.2: As we prepare to take Taylor Polynomials and extend them by taking their limit, we first want to look at what happens when we define a series using some parameter x. The results are interesting and, occasionally, unexpected.
- Extra: Just a tangent to tie together a lot of the material you have seen this year and some that you will see next year. I hope you find it interesting.