Science:Infinite Series Module/Units/Unit 3/3.2 Taylor Series

What This Lesson Covers

In this lesson we will introduce a few concepts:

• representation of functions with a power series
• conditions for convergence of a power series
• radius of convergence of a power series

Learning Objectives

After reading this lesson and completing a sufficient number of exercices on paper, you should be able to

• expand a given function in a Maclaurin series
• determine the radius of convergence of a Taylor series

Topics

1. A motivating problem
2. The Taylor and Maclaurin expansions
3. The Maclaurin expansion of e^x
4. The Maclaurin expansion of sin(x)
5. The Maclaurin expansion of cos(x)
6. A list of Maclaurin expansions
7. Videos on Taylor Series