Unit 9 - Taylor Polynomials and Power Series - Sections 10.1 and 10.2

Module Overview

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.

Learning Outcomes

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.

Type: Video Links
Title	Author	Description
Taylor Polynomials - A Re-Introduction to Linear Approximation \| Taylor Polynomials - A Re-Introduction to Linear Approximation	Shai Cohen
Taylor Polynomials - Approximating with Polynomials: A Specific Case \| Taylor Polynomials - Approximating with Polynomials: A Specific Case	Shai Cohen
Taylor Polynomials - Approximating with Polynomials: In General \| Taylor Polynomials - Approximating with Polynomials: In General	Shai Cohen
Taylor Polynomials - Defining Taylor Polynomials \| Taylor Polynomials - Defining Taylor Polynomials	Shai Cohen
Taylor Polynomials - Defining Taylor Polynomials \| Taylor Polynomials - Defining Taylor Polynomials	Shai Cohen
Taylor Polynomials - Taylor's Theorem \| Taylor Polynomials - Taylor's Theorem	Shai Cohen
Taylor Polynomials Example - The Exponential Function \| Taylor Polynomials Example - The Exponential Function	Shai Cohen
Taylor Polynomials Example - Polynomials \| Taylor Polynomials Example - Polynomials	Shai Cohen
Taylor Polynomials Example - Related Functions \| Taylor Polynomials Example - Related Functions	Shai Cohen
Taylor Polynomials Example - Approximating a Value \| Taylor Polynomials Example - Approximating a Value	Shai Cohen
Taylor Polynomials Example - The Remainder Term \| Taylor Polynomials Example - The Remainder Term	Shai Cohen
Power Series - Definition \| Power Series - Definition	Shai Cohen
Power Series - The Radius and Interval of Convergence \| Power Series - The Radius and Interval of Convergence	Shai Cohen
Power Series - Three Cases for the Radius of Convergence \| Power Series - Three Cases for the Radius of Convergence	Shai Cohen
Power Series - Combining Power Series \| Power Series - Combining Power Series	Shai Cohen
Power Series - Properties of Power Series \| Power Series - Properties of Power Series	Shai Cohen
Power Series - A Very Useful Power Series \| Power Series - A Very Useful Power Series	Shai Cohen
Radius of Convergence Example - Some Familiar Functions \| Radius of Convergence Example - Some Familiar Functions	Shai Cohen
Radius of Convergence Example - Another Familiar Function \| Radius of Convergence Example - Another Familiar Function	Shai Cohen
Radius of Convergence Example - Another Example and Some Observations \| Radius of Convergence Example - Another Example and Some Observations	Shai Cohen
Combining Power Series Example \| Combining Power Series Example	Shai Cohen
Extra - Calculus, Lin Alg, Physics, and Statistics \| Extra - Calculus, Lin Alg, Physics, and Statistics	Shai Cohen